Principles of Microeconomics

Firm Objectives and Profit Maximization

A firm’s primary goal is profit maximization – the difference between what it earns from selling output and what it spends on inputs. This assumption holds because even non‑profit or impact‑driven firms must eventually generate positive profits to remain financially sustainable.

$\text{Profit} = \text{Total Revenue} - \text{Total Cost}$

• Total Revenue (TR) = amount received from selling output
  – For a single price: $TR = P \times Q$
  – If different batches are sold at different prices, sum over each batch: $TR = \sum (P_i \times Q_i)$

• Total Cost (TC) = market value of all inputs used, including opportunity costs.

Total Revenue and Total Cost – Example (Nidhi’s Samosa Shop)

Day	Sales	Price (₹)	Revenue (₹)
Monday	1000 samosas	50	$1000 \times 50 = 50,\!000$
Tuesday	1000 samosas @ 50 + 500 catering @ 40	–	$50,\!000 + 20,\!000 = 70,\!000$

On Tuesday the additional revenue from selling 500 extra samosas at ₹40 each was ₹20,000.

Costs for Monday: raw materials, labour, rent, electricity = ₹20,000 (explicit). But Nidhi also forgoes a daily wage of ₹10,000 as a computer programmer – this is an opportunity cost. Her ₹5,00,000 capital invested at 8% p.a. gives up ₹40,000 annual interest – another opportunity cost.

Explicit vs. Implicit Costs, Accounting vs. Economic Profit

• Explicit costs – direct monetary outlays (e.g., wages, rent, raw materials).
• Implicit costs – opportunity costs of using owner‑supplied resources (e.g., forgone salary, forgone interest).

$\text{Economic cost} = \text{Explicit costs} + \text{Implicit costs}$

$\text{Accounting profit} = TR - \text{Explicit costs only}$

$\text{Economic profit} = TR - \text{Economic cost}$

• Because economic cost always ≥ accounting cost, economic profit ≤ accounting profit.
• When economic profit is positive, the firm is covering all costs and rewarding owners. Negative economic profit (loss) means the firm fails to cover its full costs.

Exam tip: A question may ask you to distinguish accounting vs. economic profit. The key is whether implicit opportunity costs are included. For simplicity in later modules, opportunity costs are often assumed zero, making the two profits equal.

Production Function and Marginal Product

Production function = relationship between quantity of inputs (labour, capital) and maximum output attainable, holding other inputs fixed.

Example: Nidhi’s kitchen size is fixed (short run). Only the number of workers can vary.

Workers (L)	Samosas per hour (Q)	Marginal Product of Labour (MPL)
0	0	–
1	50	50
2	90	40
3	120	30
4	140	20
5	150	10

Marginal product of an input $=$ change in output resulting from a one‑unit change in that input:

$MP_L = \frac{\Delta Q}{\Delta L}$

• From 0→1 workers: $MP = 50$
• From 1→2 workers: $MP = 90 - 50 = 40$
• etc.

Diminishing Marginal Product

As more workers join a fixed‑sized kitchen, each additional worker adds less to output – the diminishing marginal product:

• Reason: Crowding limits access to equipment and raw materials; greater coordination cost reduces individual productivity.
• Despite falling MP, total output still rises with each extra worker (output increases, but at a decreasing rate).

Graphically, the production function becomes flatter as L increases – slope = $MP_L$ decreases.

flowchart LR
    A[Diminishing MP] --> B[Each extra worker adds less output]
    B --> C[To raise output further, need even more workers]
    C --> D[Labour cost increases per additional unit of output]
    D --> E[Total cost curve gets steeper]

Total Cost Curve and Its Shape

Nidhi’s costs:

• Fixed cost: kitchen rent = ₹3000/hour (independent of output).
• Variable cost: wage = ₹1000 per worker per hour.
• $TC = FC + VC$

L	Q (samosas/hr)	FC (₹)	VC (₹)	TC (₹)
0	0	3000	0	3000
1	50	3000	1000	4000
2	90	3000	2000	5000
3	120	3000	3000	6000
4	140	3000	4000	7000
5	150	3000	5000	8000

• The total cost curve (TC vs. Q) slopes upward and becomes steeper as output rises.
• Reason: Because of diminishing MP, each extra samosa requires hiring more workers than the previous one, so the additional cost (marginal cost) increases.

Worked example – rising marginal cost:

• First 50 samosas: cost increase = ₹1000 (from 3000 to 4000) → ₹20 per samosa.
• Next 40 samosas (50→90): cost increase = ₹1000 → ₹25 per samosa.
• Next 30 samosas (90→120): cost increase = ₹1000 → ₹33.3 per samosa.

Thus the cost curve gets steeper as Q rises – a direct consequence of diminishing marginal product.

Key takeaways

• A firm maximizes profit = total revenue – total cost (including opportunity cost).
• Economic profit is smaller than accounting profit because it subtracts implicit costs.
• Production function maps inputs to output; marginal product measures output change from one more unit of input.
• Most production processes exhibit diminishing marginal product – the production function flattens.
• Diminishing marginal product makes the total cost curve steeper as output increases, because additional units cost more to produce.

Variable, Fixed, and Sunk Costs

Not all costs behave the same. Some rise with every extra unit you produce; others stay fixed no matter how much you make. And some are gone the moment you pay them — they can never be recovered by a production decision. Understanding these categories is essential for calculating profit and choosing the right output level.

The three cost types

A firm’s explicit costs can be divided into three categories based on how they respond to the quantity of output $Q$.

Category	Behaviour	Example from Ola Scooter factory
Variable cost	Changes with $Q$ – more output means more of these inputs	Raw materials (batteries, wheels), electricity, water, daily-wage workers
Fixed cost	Does not change with $Q$ – must be paid even if output is zero; can only be eliminated by shutting down the business entirely	Rent on land, assembly line maintenance, health insurance for permanent managers, HR department
Sunk cost	Already committed and cannot be recovered by changing the output decision	R&D spending, cost of obtaining a business license

Key insight: Fixed costs are unavoidable at any positive output, but they are still part of the total cost that affects profit. Sunk costs, by contrast, are irrelevant for any future production decision — they can never be undone, so they are excluded from the profit calculation.

How to classify a cost input

The flowchart below gives a decision rule for sorting any input cost:

flowchart LR
    A[Input cost] --> B{Unavoidable<br>even when Q = 0?}
    B -- Yes --> C[Sunk cost]
    B -- No --> D{Avoidable when Q = 0}
    D -- Varies with Q --> E[Variable cost]
    D -- Does not vary with Q --> F[Fixed cost]

• Sunk cost: The cost is already paid and cannot be retrieved — e.g., R&D, permit fees.
• Variable cost: The cost can be avoided by setting $Q = 0$, and it grows as output rises — e.g., raw materials, hourly labour.
• Fixed cost: The cost can also be avoided only by shutting down, but once the firm operates, it does not depend on the output level — e.g., monthly rent, salary of permanent staff.

Worked example: Arnav’s petrol pump

Arnav has already spent ₹10 lakh on a license and setup (sunk). He must decide whether to operate the pump next month.

Data for one month:

• Expected sales: 1 00 000 litres at ₹102/litre → Total revenue = ₹1 02 00 000
• Explicit costs:
  • Purchase of petrol: 1 00 000 litres × ₹100 = ₹1 00 00 000
  • Monthly wage: ₹40 000
  • Electricity: ₹30 000
  • Transportation: ₹80 000
• Implicit opportunity cost: ₹30 000 (return from investing the money elsewhere)

Calculation of total cost (excluding sunk cost):

$$\begin{aligned} \text{Total explicit cost} &= 1\,00\,00\,000 + 40\,000 + 30\,000 + 80\,000 = 1\,01\,50\,000 \\ \text{Total cost (including opportunity cost)} &= 1\,01\,50\,000 + 30\,000 = 1\,01\,80\,000 \end{aligned}$$

Profit:

$$\text{Profit} = \text{Revenue} - \text{Total cost} = 1\,02\,00\,000 - 1\,01\,80\,000 = ₹20\,000 > 0$$

Since profit is positive, Arnav should operate the pump. Notice the sunk ₹10 lakh was not included in total cost — it cannot affect the decision.

Exam tip: Fixed costs (like wages) are included because they must still be paid; sunk costs (like the license) are never added to total cost for an operating decision. A common trap is to include a sunk cost and wrongly conclude that the project is unprofitable.

Which cost dominates in different industries?

Industry	Dominant cost category	Reason
PC / laptop manufacturing	Variable costs	R&D is mature; most costs are for raw materials (microprocessors, memory chips, hard drives)
Software development	Sunk costs	After the first customer-ready version is built, variable and fixed costs are low, but the upfront R&D (engineers’ salaries, trial and error) cannot be recovered
Pizza shop	Fixed costs	Sunk costs are low, variable costs (flour, electricity) are modest, but the monthly rent of the shop and cost of ovens are large and fixed

Key takeaways

• Variable costs change with output; fixed costs do not change with output but can be avoided only by shutting down; sunk costs cannot be recovered and are irrelevant for future decisions.
• Fixed costs are part of total cost and therefore affect profit; sunk costs are excluded from total cost.
• Use the “avoidable when Q = 0?” test to classify: unavoidable → sunk; avoidable and varies with Q → variable; avoidable and does not vary with Q → fixed.
• Always include implicit opportunity costs when calculating economic profit.
• The dominance of one cost category varies across industries (variable→PC, sunk→software, fixed→pizza).

Short Run vs. Long Run: Fixed and Variable Costs

The classification of a cost as fixed or variable depends on the time horizon available to adjust inputs.

Intuition: With more time, a firm can change more inputs. What is “fixed” in one week can become “variable” in a year.

The Ola Example

Ola Future Factory wants to increase daily scooter production from 1,000 to 3,000.

Time frame	Feasible actions	Fixed inputs	Variable inputs
1 week	Overtime for existing workers, buy more raw materials	Number of workers, assembly lines	Working hours (via overtime)
1 quarter	Overtime + hire & train new workers	Assembly lines	Workers, working hours
1 year	Overtime + hire + build new assembly lines	None	All inputs (workers, assembly lines, land)

• Short run: a time horizon where at least one input’s quantity cannot be changed. → Fixed inputs → Fixed costs (e.g., rent on assembly lines).
• Long run: a time horizon where all inputs can be changed. → All costs are variable.

What counts as “short run” varies by industry (e.g., a scooter factory vs. a food truck).

Short Run Total Cost

In the short run, total cost is the sum of fixed cost and variable cost:

$TC = FC + VC$

Coffee Shop Example (all numbers are illustrative)

A boutique coffee shop has hourly fixed cost (rent) of ₹50.

Output (Q)	Fixed Cost (FC) ₹	Variable Cost (VC) ₹	Total Cost (TC) ₹
0	50	0	50
1	50	50	100
2	50	78	128
3	50	98	148
4	50	112	162
5	50	130	180
6	50	150	200
7	50	175	225
8	50	204	254
9	50	242	292
10	50	300	350
11	50	385	435

Average Total Cost (ATC)

Average total cost measures the cost per unit of output:

$ATC = \frac{TC}{Q}$

The ATC curve is U‑shaped: initially falling as fixed costs are spread, then rising due to diminishing returns.

From the coffee shop data:

Q	TC	ATC
1	100	100.0
2	128	64.0
3	148	49.3
4	162	40.5
5	180	36.0
6	200	33.3
7	225	32.1
8	254	31.8
9	292	32.4
10	350	35.0
11	435	39.5

Average Fixed Cost (AFC)

Average fixed cost is the fixed cost per unit of output:

$AFC = \frac{FC}{Q}$

• AFC is downward sloping (decreases as output increases) because the same fixed cost is spread over more units.
• For the coffee shop: $AFC = \frac{50}{Q}$.

Q	AFC
1	50.0
2	25.0
3	16.7
4	12.5
5	10.0
6	8.3
7	7.1
8	6.3
9	5.6
10	5.0
11	4.5

flowchart LR
  A[FC constant] --> B[Divide by Q]
  B --> C[As Q rises, AFC falls]
  C --> D[Intuition: spreading fixed costs]

Exam tip: The U‑shape of ATC comes from two opposing forces: falling AFC (spreading fixed costs) and eventually rising average variable cost (diminishing returns). AFC always declines with output.

Key takeaways

• Fixed vs. variable classification depends on time horizon (short run vs. long run).
• Short run: $TC = FC + VC$ with positive fixed costs.
• $ATC = TC/Q$; the curve is U‑shaped.
• $AFC = FC/Q$; the curve slopes downward because fixed cost is spread over more output.
• In the long run all costs are variable (no fixed costs).

Average Variable Cost (AVC)

Average variable cost is variable cost per unit of output.
Intuitively, it measures how much of the variable input cost is “spread” over each unit produced.

$\text{AVC} = \frac{\text{Variable cost}}{\text{Quantity}} = \frac{VC}{Q}$

From the coffee‑shop example, the variable cost at each output level is divided by output:

Output $Q$	$VC$ (₹)	$\text{AVC}=VC/Q$ (₹)
1	50	50
2	78	39
3	98	$98/3 \approx 32.6$

Plotted, the AVC curve first falls, then rises – a typical U‑shape driven by diminishing marginal product (see below).

Key points

• AVC is part of average total cost: $\text{ATC} = \text{AFC} + \text{AVC}$.
• At low output, AVC may decrease (specialization gains); at high output, it increases because each extra unit requires more inputs due to diminishing returns.

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Marginal Cost (MC)

Marginal cost is the cost of producing one additional unit of output.
It tells the firm how much total cost changes when output expands by a tiny amount.

$\text{MC}(q+1) = TC(q+1) - TC(q)$

Using the same coffee shop (fixed cost = ₹50, so $TC(0)=50$):

Output $Q$	$TC$ (₹)	MC (₹) calculation	MC (₹)
0	50	–	–
1	100	$100-50$	50
2	128	$128-100$	28
3	–	(not given, but follows pattern)	–

The MC curve typically declines initially (due to increasing marginal returns) then rises, reflecting diminishing marginal product. As more variable input is added to a fixed input, extra output per additional input falls → producing one more unit requires more inputs → marginal cost rises.

Exam tip: The rising part of the MC curve is the supply curve of a perfectly competitive firm in the short run (above the shutdown point).

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Relationship Between MC and ATC

When the marginal cost curve and the average total cost curve are drawn together, three universal observations hold for most firms:

1. If $\text{MC} < \text{ATC}$, then ATC is falling.
2. If $\text{MC} > \text{ATC}$, then ATC is rising.
3. MC crosses ATC at ATC’s minimum – the efficient scale.

Intuition: ATC is an average; when the next unit costs less than the average, the average falls; when it costs more, the average rises. Therefore the crossing point must be where ATC is neither falling nor rising – the minimum.

flowchart LR
  A[MC below ATC] --> B[ATC falling]
  C[MC above ATC] --> D[ATC rising]
  E[MC = ATC] --> F[ATC at minimum]

In the coffee‑shop example, ATC is minimised at an output of 8 cups per hour – the efficient scale. Below that, high average fixed cost dominates; above that, rising average variable cost dominates.

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Long-Run Average Total Cost

In the short run, at least one input is fixed (e.g., factory size). In the long run, all inputs become variable – the firm can choose any scale of operation.

Because the firm has more freedom in the long run, it can always produce any given output at a cost no higher than in the short run. Hence the long-run average total cost curve (LRATC) lies below the short‑run average total cost curves (SRATC) at every level of output.

Each SRATC corresponds to a different level of the fixed input (e.g., a specific plant size). The LRATC is the envelope of all possible SRATC curves – it shows the lowest possible cost for each output when the firm can choose the optimal plant size.

graph TD
  subgraph SRATC curves
    SR1[SRATC (small scale)]
    SR2[SRATC (medium scale)]
    SR3[SRATC (large scale)]
  end
  LR[LRATC] -.-> SR1 & SR2 & SR3
  note["LRATC always below SRATC at any Q"]

The LRATC is also typically U‑shaped (economies of scale at low output, diseconomies at high output), but it is flatter than any individual SRATC.

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Key Takeaways

• AVC = $VC/Q$; first falls, then rises.
• MC = change in TC for one more unit; rises due to diminishing marginal product.
• MC‑ATC relationship: MC below ATC → ATC falls; MC above ATC → rises; MC crosses at ATC’s minimum (efficient scale).
• Long‑run costs: more flexibility → LRATC lies below all SRATC curves.
• Fixed vs. variable input distinction depends on the time horizon; in the long run all costs are variable.

Marginal Principle

A profit-maximizing firm in a perfectly competitive market faces three decisions:

1. What quantity to produce at the given market price?
2. When to temporarily shut down production?
3. When to exit the industry entirely?

All three are answered using marginal analysis — comparing the benefit of one more unit (marginal revenue) to its cost (marginal cost).

The Firm in a Perfectly Competitive Market

A perfectly competitive market has two defining features:

• Many buyers and many sellers — no single participant can influence price.
• Homogeneous goods — products are identical across sellers.

These features force every firm to sell at the equilibrium price determined by market supply and demand. If a firm charges above the equilibrium, buyers switch to others selling the identical good at the lower price. If a buyer offers below equilibrium, sellers refuse because many other buyers will pay the higher price.

Example: A small cattle farmer sells milk. Milk is identical across farmers, and there are many producers. The farmer must accept the prevailing market price — say ₹50 per litre.

Revenue in Perfect Competition

For a firm in perfect competition:

• Total revenue $TR = P \times Q$, where $P$ is fixed.
• Average revenue $AR = \frac{TR}{Q} = P$ — constant at all output levels.
• Marginal revenue $MR = \frac{\Delta TR}{\Delta Q} = P$ — constant at all output levels.

Thus for the cattle farmer at $P = ₹50$:

Quantity (Q)	Total Revenue (TR)	Average Revenue (AR)	Marginal Revenue (MR)
0	₹0	—	—
1	₹50	₹50	₹50
2	₹100	₹50	₹50
3	₹150	₹50	₹50
…	…	₹50	₹50
10	₹500	₹50	₹50

$AR = MR = P$ holds for any price-taking firm.

Profit-Maximizing Quantity: Total Profit Method

Profit = $TR - TC$. The firm should produce the quantity that gives the highest profit.

Using the cattle farmer’s data at $P = ₹50$:

Q	TR (₹)	TC (₹)	Profit (₹)
0	0	—	—
1	50	160	−110
2	100	175	−75
3	150	195	−45
4	200	220	−20
5	250	250	0
6	300	290	10
7	350	335	15
8	400	370	30
9	450	430	20
10	500	500	0

Profit-maximizing quantity = 8 litres → maximum profit = ₹30.

Exam tip: The total profit method is straightforward but inefficient for large output ranges. The marginal principle gives the same answer faster.

Profit-Maximizing Quantity: Marginal Principle Method

The marginal principle (first seen in Module 1):

• If $MB > MC$, doing more of the activity increases net benefit.
• If $MB < MC$, doing more decreases net benefit.

Apply to the firm:

• Marginal benefit = marginal revenue ($MR = P$).
• Marginal cost ($MC$) is the cost of producing one extra unit.
• If $MR > MC$, producing another unit raises profit.
• If $MR < MC$, producing another unit lowers profit.

For the cattle farmer ($P = MR = ₹50$):

Q	MR (₹)	MC (₹)	MR – MC (₹)	Effect on profit
1	50	10	+40	Increase
2	50	15	+35	Increase
3	50	20	+30	Increase
4	50	25	+25	Increase
5	50	30	+20	Increase
6	50	40	+10	Increase
7	50	45	+5	Increase
8	50	50	0	No change
9	50	60	−10	Decrease
10	50	70	−20	Decrease

Profit increases from Q=1 to Q=8, reaches maximum at Q=8, then falls. The profit-maximizing quantity is the largest quantity where $MR \geq MC$ — here, Q=8.

Because $MR = P$ in perfect competition, the rule simplifies:

Profit-maximizing quantity = largest $Q$ such that $P \geq MC$.

If the farmer produces fewer than 8 litres, $P > MC$ — he leaves potential profit on the table. If he produces more than 8 litres, $P < MC$ — each extra unit reduces profit.

Graphical Summary

flowchart TD
    A[Start with Q=0] --> B{Is P >= MC for next unit?}
    B -->|Yes| C[Increase Q by 1]
    C --> B
    B -->|No| D[Stop at current Q]
    D --> E[This Q is profit-maximizing]

The profit curve rises as long as $MR > MC$, peaks where $MR = MC$ (or last unit where $MR \geq MC$), and declines thereafter.

Key takeaways

• In perfect competition, $AR = MR = P$ — constant at the market price.
• Profit-maximizing quantity is found either by comparing total profit across outputs or by applying the marginal principle.
• The marginal principle rule: produce the largest quantity where $P \geq MC$.
• If $P > MC$, producing more raises profit; if $P < MC$, producing more lowers profit.
• The cattle farmer example: at $P=₹50$, profit max at Q=8, profit = ₹30.

Revenue in perfect competition

A firm in a perfectly competitive market is a price taker – it cannot influence the market price by changing its output. Therefore, for any quantity $Q$:

• Total revenue (TR) = $P \times Q$
• Average revenue (AR) = $\frac{TR}{Q} = P$
• Marginal revenue (MR) = $\frac{\Delta TR}{\Delta Q} = P$ (each additional unit sold adds exactly the price)

Thus AR = MR = P. Graphically, the revenue curves collapse into a single horizontal line at the market price $P$.

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Cost curves – shape and key intersections

The three central cost curves for a firm are:

• Average total cost (ATC) – U‑shaped (economies then diseconomies of scale)
• Average variable cost (AVC) – U‑shaped, lies below ATC because $ATC = AVC + AFC$ (average fixed cost is positive)
• Marginal cost (MC) – increasing due to diminishing marginal product

Critical property: The MC curve intersects both ATC and AVC at their respective minimum points.

MC cuts ATC at min ATC
MC cuts AVC at min AVC

Exam tip: The order of the curves from bottom to top is always AVC, then ATC, then MC in its rising portion (except near the vertical axis). Remember: AVC is lower because it excludes fixed cost.

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Profit‑maximising quantity (marginal principle)

The firm chooses the largest quantity $Q^*$ such that $P \ge MC$ (marginal revenue = marginal cost). Because in perfect competition $P = MR$, the condition simplifies to:

$P = MC$

Why it works:

• If $Q < Q^*$: $P > MC$ → increasing output raises profit.
• If $Q > Q^*$: $P < MC$ → decreasing output raises profit.
• At $Q = Q^*$: $P = MC$ → profit is maximised.

The supply curve of the firm is therefore its marginal cost curve – as price rises, the profit-maximising quantity moves up along the MC curve.

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Picturing profit – revenue and cost rectangles

With the cost curves and the price line $P_0$, profit can be visualised as the difference of two rectangles:

• Total revenue = $P_0 \times Q_0$ → green rectangle (height $P_0$, width $Q_0$)
• Total cost = $ATC(Q_0) \times Q_0$ → red rectangle (height $ATC$, width $Q_0$)
• Profit = $(P_0 - ATC(Q_0)) \times Q_0$ → striped rectangle

$$\pi = Q \cdot (P - ATC)$$

Price situation	Profit sign	Condition
$P > \min ATC$	Positive	Green area > red area
$P = \min ATC$	Zero (break‑even)	Green = red
$P < \min ATC$	Negative (loss)	Red area > green area

Worked example (transcript’s exercise):

• Price $P_1$ above min ATC → green rectangle larger than red rectangle → positive profit.
• Price $P_2$ below min ATC but above min AVC → green rectangle smaller than red rectangle → loss, but firm may still operate in short run (see below).

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Short‑run shutdown decision (temporary)

In the short run, fixed costs are sunk – they must be paid regardless of production. The firm compares total revenue with total variable cost:

$\text{Shut down temporarily if } TR < TVC$

Dividing by $Q$ gives the shutdown rule:

$\boxed{P < AVC}$

• If $P > AVC$: operate even if making losses, because revenue covers variable costs and partly recovers fixed costs.
• If $P < AVC$: shut down immediately; producing adds loss beyond sunk fixed costs.

Graphically: The short‑run supply curve is the portion of the MC curve lying above the AVC curve. For any price below the minimum AVC, quantity supplied = 0.

flowchart TD
    A[Market price P] --> B{P > AVC?}
    B -->|Yes| C[Produce where P = MC\nPositive or negative profit possible]
    B -->|No| D[Shut down: Q=0\nLoss = fixed cost only]

Exam tip: A firm can be making losses but still operate in the short run – as long as price covers average variable cost. The shutdown point is the minimum AVC, not the minimum ATC.

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Long‑run exit decision (permanent)

In the long run, all costs are variable – no sunk costs. The firm can sell off assets and avoid fixed costs entirely. The decision rule becomes:

$\text{Exit if } TR < TC$

Dividing by $Q$:

$\boxed{P < ATC}$

• If $P > ATC$: enter the industry (positive profits).
• If $P < ATC$: exit (losses cannot be recovered).

The long‑run supply curve of the firm is the portion of the MC curve above the ATC curve.

Decision	Condition	Outcome
Temporary shutdown (short‑run)	$P < AVC$	Q=0, fixed costs still paid
Permanent exit (long‑run)	$P < ATC$	Firm leaves industry, no obligations

Intuition: In the short run, the firm has already paid fixed costs – it will tolerate losses as long as the price covers variable costs, because shutting down entirely would waste the fixed cost recovery. In the long run, it avoids fixed costs altogether and will only stay if the price covers all costs.

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Summary of supply curves

• Short‑run supply: MC curve above $AVC$ (the part where $P \ge AVC$)
• Long‑run supply: MC curve above $ATC$ (the part where $P \ge ATC$)

The firm’s profit‑maximising behaviour is fully captured by these two supply curves.

Key takeaways

• In perfect competition, $P = MR = AR$; revenue curves are a horizontal line.
• Profit‑maximising quantity: $P = MC$. This defines the firm’s supply curve.
• Profit = $Q \cdot (P - ATC)$. Positive only if $P > \min ATC$.
• Short‑run shutdown rule: $P < AVC$ → stop production; otherwise operate even with losses.
• Long‑run exit rule: $P < ATC$ → leave the industry.
• The short‑run supply curve is the MC above AVC; the long‑run supply curve is the MC above ATC.

Practice Problem: Perfect Competition with Identical Firms

Given – a market with 9 identical firms, each with cost structure:

• Total cost: $TC = 50 + \frac{1}{2}Q^2$
• Marginal cost: $MC = Q$
• Market demand: $Q_d = 120 - P$

1. Fixed Cost, Variable Cost, ATC, AVC

• Fixed cost = 50 (independent of output).
• Variable cost = $\frac{1}{2}Q^2$.
• Average total cost:
  $ATC = \frac{TC}{Q} = \frac{50}{Q} + \frac{1}{2}Q$
• Average variable cost:
  $AVC = \frac{VC}{Q} = \frac{1}{2}Q$

2. Cost Curves for $Q \in [5,15]$

$Q$	$ATC$	$AVC$	$MC$
5	12.5	2.5	5
6	11.33	3	6
8	10.25	4	8
9	10.05	4.5	9
10	10	5	10
11	10.05	5.5	11
15	10.83	7.5	15

• ATC is U‑shaped, decreasing from $Q=5$ to $Q=10$, then rising.
• AVC rises linearly from 0 (at $Q=0$) – it is an increasing curve.
• MC = $Q$ is a 45° line through the origin.

3. Minimum of ATC

• Graphically: MC intersects ATC at its minimum.
• Mathematically: set $ATC = MC$
  $\frac{50}{Q} + \frac{1}{2}Q = Q \quad\Rightarrow\quad \frac{50}{Q} = \frac{1}{2}Q \quad\Rightarrow\quad Q^2 = 100 \quad\Rightarrow\quad Q = 10$
• At $Q=10$: $MC = 10$, $ATC = 10$.

  Exam tip: The condition $MC = ATC$ always locates the minimum of the average total cost curve.

4. Minimum of AVC

• $AVC = \frac{1}{2}Q$ is increasing for $Q>0$; its minimum occurs at $Q=0$.
• Set $AVC = MC$: $\frac{1}{2}Q = Q \Rightarrow Q=0$.
• At $Q=0$: $AVC = 0$, $MC = 0$.

5. Short‑Run Supply Curves

Individual firm supply: the portion of MC above the minimum AVC.
Since $MC = Q > \frac{1}{2}Q = AVC$ for all $Q>0$, the entire MC curve (from $Q=0$ upward) is the supply curve.

• Inverse supply: $P = Q$
• Supply equation: $q_i(P) = P$ (each firm supplies its marginal cost price).

Market supply with 9 firms:
$Q_s(P) = 9 \times q_i(P) = 9P$

6. Short‑Run Equilibrium

Set quantity demanded equal to quantity supplied:
$120 - P = 9P \quad\Rightarrow\quad 10P = 120 \quad\Rightarrow\quad P^* = 12$
$Q^* = 120 - 12 = 108 \quad (\text{or } 9 \times 12)$

Each firm’s output: $q_i = 108 / 9 = 12$ (consistent with $q_i = P = 12$).

Profit per firm:
$\pi = P \cdot q_i - TC(12) = 12 \times 12 - \left(50 + \frac{1}{2} \times 144\right) = 144 - (50 + 72) = 22$

• Positive profits → firms outside have incentive to enter in the long run.

7. Long‑Run Equilibrium

In long‑run perfect competition, entry drives economic profit to zero.
Zero‑profit condition: $P = \text{min } ATC$.

From earlier: min ATC = 10 at $Q=10$. Hence long‑run price $P^* = 10$.

Market demand at this price:
$Q_d = 120 - 10 = 110$

Each firm produces at its efficient scale: $q_i = 10$ (because $P=10$ and supply $q_i=P$ gives $q_i=10$).

Number of firms:
$N = \frac{Q_d}{q_i} = \frac{110}{10} = 11$

• Check zero profit: $P = 10$, $ATC = 10$, so $\pi = (10-10) \times 10 = 0$.

Key Takeaways

• Short‑run supply for a firm = MC above AVC; here $q_i = P$.
• Short‑run equilibrium found by $Q_d = Q_s$; positive profits trigger entry.
• Long‑run equilibrium occurs when $P = \min ATC$ and each firm earns zero profit.
• Fixed cost shifts ATC but does not affect short‑run supply (only AVC matters for shutdown).
• Given cost and demand, the long‑run number of firms is $N = \frac{\text{market demand at min ATC}}{\text{efficient scale}}$ (here 11 firms).

Exam tip: In long‑run perfect competition, always start by finding the minimum of ATC – that gives the long‑run price and efficient scale.

Market Equilibrium in a Competitive Market

A market consists of buyers (consumers) and sellers (producers). The demand curve (downward-sloping) shows quantity demanded at each price, ceteris paribus. The supply curve (upward-sloping) shows quantity supplied at each price, ceteris paribus. When plotted together, they intersect at a single point – the market equilibrium. The price at this point is the equilibrium price ($P^*$) and the quantity is the equilibrium quantity ($Q^*$).

At $P^*$, the quantity demanded exactly equals the quantity supplied: the market clears. No inherent force pushes price away from $P^*$; instead, self-interested behaviour of buyers and sellers drives any deviation back toward equilibrium – like a ball in a bowl returning to the bottom.

Forces Driving Toward Equilibrium: Excess Supply & Excess Demand

1. Price Above Equilibrium ($P > P^*$)

• Quantity supplied ($Q_S$) exceeds quantity demanded ($Q_D$) → excess supply (surplus).
  $\text{Excess supply} = Q_S - Q_D > 0$.
• Symptoms: inventories pile up, customers are infrequent.
• Seller response: offer discounts to clear stock → downward pressure on price.
• Process persists until price falls back to $P^*$.

2. Price Below Equilibrium ($P < P^*$)

• $Q_D$ exceeds $Q_S$ → excess demand (shortage).
  $\text{Excess demand} = Q_D - Q_S > 0$.
• Symptoms: inventories vanish quickly, long queues, waiting times.
• Seller response: some buyers offer to pay more; sellers can raise prices without losing customers → upward pressure on price.
• Process continues until price rises to $P^*$.

3. Price at Equilibrium ($P = P^*$)

• $Q_D = Q_S$. No excess demand or supply. No pressure for price to change.

flowchart TD
    P_above["Price > P*"] --> surplus["Excess Supply (Surplus)"]
    surplus --> down["Downward pressure on price"]
    down --> P_star["Price → P*"]

    P_below["Price < P*"] --> shortage["Excess Demand (Shortage)"]
    shortage --> up["Upward pressure on price"]
    up --> P_star2["Price → P*"]

Exam tip: The only price where quantity demanded equals quantity supplied is the equilibrium price. Any other price creates a surplus or shortage, which pushes the price back to $P^*$.

Worked Example: Finding Equilibrium with Linear Curves

Given:

• Inverse demand: $P_X = 25 - 0.005 Q + 0.15 P_Y$
• Inverse supply: $P_X = 5 + 0.004 Q$
• $P_Y$ is the price of a related good Y.

Part A: Equilibrium when $P_Y = 10$

1. Substitute $P_Y = 10$ into the demand equation: $P_X = 25 - 0.005 Q + 0.15 \times 10 = 26.5 - 0.005 Q$

2. At equilibrium, quantity demanded = quantity supplied. Set the two inverse curves equal: $26.5 - 0.005 Q^* = 5 + 0.004 Q^*$ $21.5 = 0.009 Q^* \quad \Rightarrow \quad Q^* = \frac{21.5}{0.009} = \frac{21500}{9} \approx 2388.89$

3. Find $P^*$ by substituting $Q^*$ into either equation (e.g., supply side): $P^* = 5 + 0.004 \times \frac{21500}{9} = 5 + \frac{86}{9} \approx 14.56$

   Thus, $P^* \approx 14.56$, $Q^* \approx 2388.89$ (pounds/week).

Part B: Are X and Y substitutes or complements?

Rewrite the demand function to see how $Q$ responds to $P_Y$: $0.005 Q = 25 - P_X + 0.15 P_Y \quad\Rightarrow\quad Q = \frac{25 - P_X + 0.15 P_Y}{0.005}$

As $P_Y$ increases, the right-hand side increases, so $Q$ increases. This means a rise in the price of Y raises demand for X – goods X and Y are substitutes (used in place of each other).

Part C & D: New equilibrium when $P_Y = 20$

1. Substitute $P_Y = 20$ into demand: $P_X = 25 - 0.005 Q + 0.15 \times 20 = 28 - 0.005 Q$

2. Equate with supply: $28 - 0.005 Q^*_N = 5 + 0.004 Q^*_N \quad\Rightarrow\quad 23 = 0.009 Q^*_N \quad\Rightarrow\quad Q^*_N = \frac{23000}{9} \approx 2555.56$

3. Find new price $P^*_N$ using supply: $P^*_N = 5 + 0.004 \times \frac{23000}{9} = 5 + \frac{92}{9} \approx 15.22$

4. Compare old ($P^* \approx 14.56$) and new ($P^*_N \approx 15.22$): the new equilibrium price is higher. At the old price $P^*$, after the shift in demand (due to higher $P_Y$), there will be excess demand because buyers now want more at that price than sellers are willing to supply. (Exact calculation left as exercise.)

The Invisible Hand of Prices

Even without a central planner, competitive markets achieve coordination – a feature called the invisible hand of prices. Prices simultaneously:

• Ration scarce resources – e.g., housing in Mumbai: price adjusts until only those willing and able to pay get housing.
• Allocate production – higher expected fish prices attract more fishermen; price signals determine who becomes a seller and how much to produce.
• Coordinate buyers and sellers – if price is too low, shortage pushes it up; if too high, surplus pushes it down – all through self-interested actions.

This spontaneous order is a striking property of perfectly competitive markets. Prices contain all necessary information for individuals to act, achieving equilibrium without central control.

Exam tip: The invisible hand is not a physical force; it describes how the price mechanism guides self-interested decisions toward a socially coordinated outcome (market clearing). Be prepared to explain with real-world examples like fish markets, housing, or agricultural produce.

Key Takeaways

• Market equilibrium: $Q_D = Q_S$ at $P^*$; the only point with no inherent pressure to change.
• Prices above $P^*$ create surplus → downward pressure; prices below $P^*$ create shortage → upward pressure.
• The adjustment process is automatic, driven by seller responses to inventory/build-up and buyer competition.
• Equilibrium is found by setting quantity demanded equal to quantity supplied (or inverse curves equal).
• Related goods: if demand for X increases when $P_Y$ rises, X and Y are substitutes.
• The invisible hand of prices coordinates the actions of many independent buyers and sellers, allocating resources without central authority.

Market Equilibrium: Real World Examples

The market equilibrium model (supply meeting demand) isn't just theory — it predicts real price changes. A four‑step checklist turns any news event into a prediction:

flowchart LR
  A[1. Identify the market(s)] --> B[2. Does the event shift supply, demand, or both?]
  B --> C[3. Determine direction of each shift]
  C --> D[4. Use S&D diagram → new equilibrium P and Q]

Four‑step checklist

1. Market – which good(s) are we analysing?
2. Curve shift – does the event affect supply (production cost, technology, number of sellers) or demand (tastes, income, prices of related goods)?
3. Direction – left (decrease) or right (increase)?
4. New equilibrium – combine shifts in a supply‑and‑demand diagram to get new price and quantity.

Exam tip: Step 2 is the most error‑prone. Always ask: does the event change producers’ costs/ability to sell, or consumers’ willingness to buy? Never guess — use the standard shift determinants.

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Example 1: Fire at an auto‑chip plant → new car prices (India, March 2021)

The news: A fire destroys a major semiconductor chip plant.
Step 1 – Markets: Semiconductor chips → new cars.
Step 2 – Supply or demand?

• Chips: production capacity destroyed → supply shifts left. Demand unchanged.
• New cars: chips are an input. Input price rises → supply of new cars shifts left. Demand unchanged (no direct effect on consumer preferences).

Step 3 – Direction: Both supply curves shift left (decrease).
Step 4 – Result: Equilibrium price of new cars increases; equilibrium quantity decreases.

This analysis tells the Honda manager: expect higher car prices in coming months.

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Example 2: New car price rise → used car market (India)

The news: As above, new car prices will rise.
Step 1 – Market: Used cars.
Step 2 – Curve shift?

• Supply of used cars – unaffected (semiconductor fire doesn’t change stock of used cars).
• Demand for used cars – new cars and used cars are substitutes. Higher price of new cars → consumers switch → demand for used cars shifts right.

Step 3 – Direction: Demand right, supply unchanged.
Step 4 – Result: Used car price increases; quantity increases.

Exam tip: Substitutes link markets. When the price of good A rises, demand for substitute B shifts right — always check for cross‑market effects.

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Example 3: Russia‑Ukraine war (Feb 2022) → crude oil & cotton prices

The event: Russia is a large crude‑oil supplier; war reduces oil supply.

Step 1 – Markets involved

• Crude oil (primary market)
• Synthetic fibres (nylon, polyester) – an intermediate market
• Cotton (final market, substitute for synthetic fibres)

Step 2 & 3 – Shifts and directions

Market	Shock	Curve shifted	Direction	Reason
Crude oil	War reduces Russian oil supply	Supply	Left	Supplier capacity lost
Synthetic fibres	Crude oil is a key input; its price rises	Supply	Left	Higher input cost
Cotton	Synthetic fibre price rises (substitute)	Demand	Right	Consumers switch to cotton

Step 4 – New equilibrium prices

Market	Old price	New price	Effect
Crude oil	$P_O^*$	$P_O^{**}$	Increases
Synthetic fibres	$P_S^*$	$P_S^{**}$	Increases
Cotton	$P_C^*$	$P_C^{**}$	Increases

The shock propagates:
$\text{Crude oil supply ↓} \rightarrow \text{Oil price ↑} \rightarrow \text{Synthetic fibre supply ↓} \rightarrow \text{Synthetic fibre price ↑} \rightarrow \text{Cotton demand ↑} \rightarrow \text{Cotton price ↑}$

This explains the WSJ observation: crude oil and cotton prices move together — because crude oil indirectly affects cotton via the synthetic‑fibre substitute channel.

Exam tip: A shock in one market can “travel” through related markets. Always trace the chain: input markets → producer goods → substitutes/complements. A left shift in supply upstream can create a right shift in demand downstream.

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Key takeaways

• Use the four‑step checklist: Market → Supply or demand? → Direction → New equilibrium.
• Input price increases shift supply left; substitute price increases shift demand right.
• One event can affect multiple markets sequentially (e.g., chip fire → new cars → used cars; war → oil → synthetics → cotton).
• Predictions are directional (price up/down), not numerical. The model gives qualitative trends.

Consumer Surplus

Consumer surplus measures the benefit buyers receive from participating in a market. Intuitively: a buyer is willing to pay up to a certain amount for a good (the value they place on it), but often pays less. The gap between what they’d pay and what they actually pay is their surplus – a direct measure of gain.

Formal definition

Consumer surplus = Willingness to pay – Amount actually paid

• Willingness to pay (WTP) – the maximum price a buyer would pay for a good; reflects the monetary value of the utility they expect from consuming it.
• Amount paid – the market price (or auction price) they actually hand over.

If a buyer does not purchase, their consumer surplus is zero (no gain, no loss).

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Worked example: single‑ticket auction

Three friends – Sanju, Rahul, Shreyas – bid for one IPL final ticket.

Buyer	Willingness to pay (₹)
Sanju	10,000
Rahul	8,000
Shreyas	5,000

Auction starts at ₹3,000; bids rise. Sanju wins with a bid just above ₹8,000 (Rahul and Shreyas drop out at ₹8,000).
Sanju pays ₹8,000 for a ticket he values at ₹10,000.

$\text{Sanju’s consumer surplus} = 10,\!000 - 8,\!000 = 2,\!000 \text{ rupees}$

Rahul and Shreyas get zero surplus.

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Worked example: two tickets (uniform price)

Two tickets auctioned at the same price. Bidding stops when Sanju and Rahul bid just above ₹5,000; Shreyas drops out.

• Sanju gets a ticket at ₹5,000 (WTP ₹10,000) → surplus = ₹5,000.
• Rahul gets a ticket at ₹5,000 (WTP ₹8,000) → surplus = ₹3,000.
• Shreyas gets nothing → surplus = ₹0.

$\text{Total consumer surplus} = 5,\!000 + 3,\!000 = 8,\!000 \text{ rupees}$

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Consumer surplus on the demand curve

The demand curve for three buyers (step function) shows the willingness to pay of the marginal buyer at each quantity.

Price range (₹)	Quantity demanded	Marginal buyer (WTP)
Above 10,000	0	–
8,000 – 10,000	1	Sanju (₹10,000)
5,000 – 8,000	2	Rahul (₹8,000)
Below 5,000	3	Shreyas (₹5,000)

The height of the demand curve at a given quantity equals the WTP of the marginal buyer (the one who would exit the market at a slightly higher price).

Measuring consumer surplus graphically

At any price $P$, consumer surplus is the area below the demand curve and above the price, up to the quantity traded.

• Single ticket at ₹8,000: area = rectangle 2,000 × 1 = ₹2,000 (Sanju’s surplus).
• Two tickets at ₹5,000: area = two rectangles – Sanju’s (5,000 × 1) and Rahul’s (3,000 × 1) – total ₹8,000.

For a smooth downward‑sloping demand curve:

• At price $P_1$, quantity $Q_1$ → consumer surplus = triangle $ABC$.
• At a lower price $P_2$, quantity $Q_2$ → consumer surplus = triangle $ADF$.

Effect of a price decrease

Lowering price from $P_1$ to $P_2$ increases consumer surplus through two channels:

1. Existing buyers who already purchased at $P_1$ now pay less → gain rectangle $(P_1 - P_2) \times Q_1$.
2. New buyers (who valued the good between $P_2$ and $P_1$) now enter the market → gain triangle with base $(Q_2 - Q_1)$ and height $(P_1 - P_2)$.

flowchart LR
  A[Price falls from P1 to P2] --> B[Existing buyers pay less]
  A --> C[New buyers enter]
  B --> D[Rectangular surplus gain]
  C --> E[Triangular surplus gain]
  D & E --> F[Total consumer surplus increases]

Exam tip: Consumer surplus ≠ profit. It measures buyer welfare, not seller revenue. On a graph, always shade the area below demand and above the market price – that's the surplus.

Key takeaways

• Consumer surplus = willingness to pay – price paid.
• It captures the benefit buyers get from trading at a price lower than their maximum.
• Graphically: area below the demand curve and above the price.
• A price drop increases surplus both for existing buyers (rectangular gain) and new buyers (triangular gain).
• The demand curve's height at each quantity shows the marginal buyer's willingness to pay – the last buyer who would still buy at that price.

Producer Surplus

Producer surplus (PS) measures the economic benefit a seller receives from selling a good. Intuitively: a seller has a minimum acceptable price (their cost). If they actually get a higher price, the difference is pure gain — their surplus. The concept mirrors consumer surplus but on the supply side.

Definition and Example

$\text{Producer Surplus} = \text{Price received} - \text{Seller's cost}$

A seller’s cost includes all out‑of‑pocket expenses plus the opportunity cost of their time. It is the lowest price they would accept — their willingness to sell.

Three painters, one room

Seller	Cost (₹)	Willing to sell at price ≥
Shreyas	3,000	₹3,000
Rahul	4,000	₹4,000
Sanju	5,000	₹5,000

An auction for painting one room starts high; bidders drop out as price falls. The price settles at just below ₹4,000 — below Rahul’s cost but above Shreyas’s cost. Only Shreyas accepts.

• Shreyas receives ≈ ₹4,000, his cost is ₹3,000.
  $\text{PS} = 4{,}000 - 3{,}000 = ₹1{,}000$.
• Rahul and Sanju do not work → no payment, no cost → PS = ₹0 each.
• Total PS = ₹1,000.

Two rooms, same painters

Now two rooms must be painted; each painter can do at most one room, and both rooms are paid the same price. The auction stops when the price reaches just below ₹5,000. At that price:

• Shreyas (cost ₹3,000) and Rahul (cost ₹4,000) are willing.

• Sanju (cost ₹5,000) drops out.

• Shreyas: $\text{PS} = 5{,}000 - 3{,}000 = ₹2{,}000$.

• Rahul: $\text{PS} = 5{,}000 - 4{,}000 = ₹1{,}000$.

• Sanju: PS = ₹0.

• Total PS = ₹3,000.

Exam tip: In the multi‑seller case, total producer surplus is the sum of individual surpluses. Only sellers who actually transact earn surplus.

Supply Schedule and Supply Curve

The supply schedule shows quantity supplied at each price. From the three painters:

Price range	Quantity supplied	Sellers willing
$P < 3{,}000$	0	None
$3{,}000 \le P < 4{,}000$	1	Shreyas
$4{,}000 \le P < 5{,}000$	2	Shreyas, Rahul
$P \ge 5{,}000$	3	Shreyas, Rahul, Sanju

Plotting this gives a step‑function supply curve. The height of each step equals the cost of the marginal seller — the one who would exit if price fell further:

• At $Q=1$, height = ₹3,000 (Shreyas’s cost).
• At $Q=2$, height = ₹4,000 (Rahul’s cost).
• At $Q=3$, height = ₹5,000 (Sanju’s cost).

Producer Surplus as Area Below Price and Above Supply

For any price $P$, producer surplus = area below $P$ and above the supply curve, up to the quantity traded.

Step‑function case

• Single room, $P = ₹4{,}000$, $Q=1$
  Area = rectangle of height $(4{,}000 - 3{,}000) = 1{,}000$, width 1 → ₹1,000 (Shreyas’s surplus).

• Two rooms, $P = ₹5{,}000$, $Q=2$
  Area splits into two rectangles:

  • Blue: $(5{,}000 - 3{,}000) \times 1 = ₹2{,}000$ (Shreyas).
  • Red: $(5{,}000 - 4{,}000) \times 1 = ₹1{,}000$ (Rahul).
    Total = ₹3,000.

Smooth upward‑sloping supply curve

In a market with many sellers, the supply curve becomes smooth. At price $P_1$ and quantity $Q_1$, producer surplus is triangle ABC (area below $P_1$, above supply).

If price rises to $P_2 > P_1$, new equilibrium quantity $Q_2$. The increase in producer surplus decomposes into three parts:

flowchart LR
  A[Price increase P1→P2] --> B[Existing sellers gain: rectangle BCED]
  A --> C[New sellers enter: triangle CEF]
  B --> D[Area = Q1 × (P2−P1)]
  C --> E[Area = ½ × (Q2−Q1) × (P2−P1)]

• Triangle ABC – original PS at $P_1$.
• Rectangle BCED – extra surplus for the $Q_1$ existing sellers (each gets $P_2 - P_1$ more).
• Triangle CEF – surplus of $(Q_2 - Q_1)$ new sellers now willing to produce at the higher price.

Thus, higher price increases producer surplus through both intensive (higher per‑unit gain) and extensive (new sellers) margins.

Key takeaways

• $\text{PS} = \text{Price} - \text{Seller's cost}$ (cost includes opportunity cost).
• Only sellers who actually sell earn surplus; total PS = sum over all sellers.
• Graphically: PS = area below price and above the supply curve.
• For a step supply curve, each step’s height = marginal seller’s cost; area decomposes into rectangles per seller.
• A price rise boosts PS via existing sellers (rectangle) and new entrants (triangle).

Intuition and Definition

Total surplus measures society’s overall economic well‑being from a market. It combines the welfare of buyers and sellers:

$$\text{Total Surplus} = \text{Consumer Surplus} + \text{Producer Surplus}$$

Recall:

• Consumer surplus (CS) = value to buyers – price paid.
• Producer surplus (PS) = price received – cost to sellers.

Since the price paid by buyers equals the price received by sellers, these terms cancel when adding CS and PS. Thus total surplus simplifies to:

$$\boxed{\text{Total Surplus} = \text{Value to Buyers} - \text{Cost to Sellers}}$$

Intuition: Society gains when a good is produced and consumed only if its value to the buyer exceeds the seller’s cost of producing it. Total surplus is the sum of those net gains across all units traded.

Graphical Representation

In a competitive market equilibrium (price $P^*$, quantity $Q^*$):

• CS = area below the demand curve and above $P^*$ (triangle $ABC$ in the figure).
• PS = area above the supply curve and below $P^*$ (triangle $DBC$).
• Total surplus = area between the demand and supply curves, up to $Q^*$ (triangle $ADC$).

Demand curve (downward sloping)
Supply curve (upward sloping)
Intersection at (Q*, P*)

Consumer surplus: triangle above P* under demand
Producer surplus: triangle below P* above supply
Total surplus: triangle from demand to supply, left of Q*

Efficiency

An allocation of resources is efficient if it maximizes total surplus. If not, it is inefficient.

Three symptoms of inefficiency (each illustrated by the transcript’s examples):

1. Unrealised gains from trade – Some mutually beneficial transactions do not occur.
   Example: Keeping an IPL ticket instead of selling it; total surplus is zero instead of positive.

2. Goods not allocated to the highest‑value buyers – A buyer with a lower willingness to pay receives the good, while a higher‑value buyer does not.
   Example: Selling the IPL ticket to Shreyas (WTP ₹5,000) instead of Sanju (WTP ₹10,000) reduces total surplus from ₹10,000 to ₹5,000.

3. Goods not produced by the lowest‑cost sellers – A seller with higher cost produces, while a lower‑cost seller does not.
   Example: Giving the painting job to Sanju (cost ₹5,000) instead of Shreyas (cost ₹3,000) reduces total surplus from ₹4,000 to ₹2,000.

Why Market Equilibrium is Efficient

The competitive equilibrium (where demand = supply) automatically avoids all three inefficiencies.

1. All gains from trade are realised

• At any quantity $Q < Q^*$, the value to buyers (height of demand) exceeds cost to sellers (height of supply). Producing these units adds positive surplus.
• At any $Q > Q^*$, cost exceeds value – producing those units would reduce total surplus.
• The equilibrium quantity $Q^*$ is exactly where value = cost on the marginal unit, so no gains are left unrealised and no wasteful units are produced.

2. Goods go to the highest‑value buyers

• In equilibrium, the good is bought only by consumers whose willingness to pay is at least $P^*$ (points on the demand curve at and above $A$–$C$). Buyers with lower willingness to pay choose not to purchase.

3. Goods are produced by the lowest‑cost sellers

• Only sellers whose cost is at most $P^*$ supply the good (points on the supply curve at and below $B$–$C$). Higher‑cost sellers choose not to produce.

Because the equilibrium achieves all three properties, it maximises total surplus. A benevolent central planner would have no reason to alter the market outcome.

Exam tip: Efficiency of a competitive market is one of the most important results in microeconomics. Be ready to explain (i) why $Q^*$ maximises total surplus, (ii) how the price mechanism allocates goods to those who value them most, and (iii) why production is done by the cheapest sellers. The three inefficiency symptoms often appear in welfare analysis questions.

Key Takeaways

• Total surplus = value to buyers – cost to sellers = CS + PS.
• An efficient allocation maximises total surplus.
• Inefficiency arises from unrealised trades, misallocation to low‑value buyers, or production by high‑cost sellers.
• In a competitive equilibrium, all three problems are automatically solved: $Q^*$ maximises surplus, buyers with highest WTP purchase, and sellers with lowest cost produce.
• Hence the market is efficient without any central planner intervention.

Price Elasticity of Demand

Price elasticity of demand (PED) measures how responsive the quantity demanded of a good is to a change in its own price. The law of demand tells only the direction of change (price up → quantity down), but not the magnitude. Managers and policymakers need a quantitative measure:

• A pricing manager deciding whether to raise refrigerator prices when costs rise must know how much sales will drop.
• A government trying to cut cigarette consumption by 20% via a tax needs to set the tax such that the resulting price hike reduces quantity by exactly 20%.

PED supplies that measure.

Formal definition

Holding all other determinants of demand constant,

$$\text{PED} = \frac{\%\,\Delta Q_d}{\%\,\Delta P}$$

where

$$\%\,\Delta P = \frac{P_2 - P_1}{P_1} \times 100,\qquad \%\,\Delta Q_d = \frac{Q_2 - Q_1}{Q_1} \times 100$$

Because price and quantity move in opposite directions (law of demand), the signs of the two percentage changes are always opposite → PED is always negative. To simplify interpretation, economists work with the absolute value:

$$\lvert\text{PED}\rvert = \frac{\lvert\%\,\Delta Q_d\rvert}{\lvert\%\,\Delta P\rvert}$$

Interpreting the number

$\lvert\text{PED}\rvert$	Classification	Meaning	Curve shape
$0$	Perfectly inelastic	Quantity does not change at all with price	Vertical
$<1$	Inelastic	$\%\,\Delta Q < \%\,\Delta P$ – demand not very sensitive	Steep
$1$	Unitary elastic	$\%\,\Delta Q = \%\,\Delta P$ – theoretical benchmark	—
$>1$	Elastic	$\%\,\Delta Q > \%\,\Delta P$ – demand very sensitive	Flat
$\infty$	Perfectly elastic	Any price increase above $P^*$ → quantity falls to zero	Horizontal

Worked example

Consider two markets. In both, price rises by 10%.

• Market 1: Quantity falls by 20%.
  $\lvert\text{PED}\rvert = 20/10 = 2$ → elastic.
• Market 2: Quantity falls by 40%.
  $\lvert\text{PED}\rvert = 40/10 = 4$ → even more elastic.

The same price change causes a larger quantity response in Market 2; higher elasticity means greater responsiveness.

Relationship with the slope of the inverse demand curve

The inverse demand curve expresses price as a function of quantity, e.g. $P = A - BQ$. Slopes of these curves relate to elasticity:

flowchart LR
  A[Vertical demand] -->|PED = 0| B[Perfectly inelastic]
  C[Steep demand] -->|0 < PED < 1| D[Inelastic]
  E[Flat demand] -->|PED > 1| F[Elastic]
  G[Horizontal demand] -->|PED = ∞| H[Perfectly elastic]

Rule of thumb: The steeper the inverse demand curve through a point, the lower the elasticity; the flatter it is, the higher the elasticity.

Exam tip: Do not confuse elasticity with slope. Slope measures absolute changes ($\Delta P / \Delta Q$), while elasticity measures percentage changes. A vertical curve has infinite slope but zero elasticity; a horizontal curve has zero slope but infinite elasticity.

Key takeaways

• PED $= \frac{\%\Delta Q}{\%\Delta P}$; use absolute values because the sign is always negative.
• Elastic if $>1$, inelastic if $<1$, unit elastic if $=1$.
• Perfectly inelastic ($\text{PED}=0$) → vertical demand; perfectly elastic ($\text{PED}=\infty$) → horizontal demand.
• Steeper demand → lower elasticity; flatter demand → higher elasticity.
• PED quantifies how much quantity responds to price, solving problems where only direction (law of demand) is not enough.

Elasticity and Linear Demand Curve

Price elasticity of demand (PED) measures how responsive quantity demanded is to a price change. For a linear inverse demand curve, elasticity varies at every point—it is not constant—and we can partition the curve into distinct zones.

Deriving Elasticity for a Linear Inverse Demand Curve

The inverse demand curve is:
$P = A - BQ, \quad A,B > 0$

Let the initial point be $(P_1, Q_1)$ with $Q_1 = (A - P_1)/B$. After a price increase to $P_2$, quantity falls to $Q_2 = (A - P_2)/B$. Compute the absolute percentage changes:

• $\% \Delta P = \frac{P_2 - P_1}{P_1}$
• $\% \Delta Q = \frac{Q_1 - Q_2}{Q_1} = \frac{(A-P_1)/B - (A-P_2)/B}{Q_1} = \frac{P_2 - P_1}{B Q_1}$

Then elasticity is: $E_d = \frac{\% \Delta Q}{\% \Delta P} = \frac{(P_2 - P_1)/(B Q_1)}{(P_2 - P_1)/P_1} = \frac{P_1}{B Q_1}$

Generalising to any point $(P,Q)$ on the linear curve: $E_d = \frac{1}{B} \cdot \frac{P}{Q}$

Since $P = A - BQ$, substitute to get an expression in $Q$ only: $E_d = \frac{A}{BQ} - 1$

How Elasticity Varies Along the Curve

Because $E_d = A/(BQ) - 1$, it decreases as $Q$ increases. The following table summarises the five zones:

Condition on $Q$	$E_d$	Zone	Meaning
$Q = 0$	$\infty$	Perfectly elastic	Any price rise collapses quantity to zero
$0 < Q < \frac{A}{2B}$	$>1$	Elastic	$\% \Delta Q > \% \Delta P$
$Q = \frac{A}{2B}$	$=1$	Unitary elastic	$\% \Delta Q = \% \Delta P$
$\frac{A}{2B} < Q < \frac{A}{B}$	$0 < E_d < 1$	Inelastic	$\% \Delta Q < \% \Delta P$
$Q = \frac{A}{B}$	$0$	Perfectly inelastic	Quantity fixed, price change has no effect

The corresponding price at the midpoint ($Q = A/(2B)$) is $P = A/2$; at the intercepts, $P = A$ when $Q=0$, and $P=0$ when $Q = A/B$.

Exam tip: For a linear demand curve, the midpoint is always the point of unit elasticity. Above the midpoint demand is elastic; below it is inelastic. This is a classic test item.

Worked Example: Recovering the Linear Demand Curve from a Point and Elasticity

Problem: Tata Motors expects to sell 2 lakh cars at a price of 20 lakhs per car, with a price elasticity of 2. Find the linear inverse demand curve (assumed linear).

Solution:
Let inverse demand be $P = A - BQ$. At $(P,Q) = (20, 2)$: $E_d = \frac{1}{B} \cdot \frac{P}{Q} \quad \Rightarrow \quad 2 = \frac{1}{B} \cdot \frac{20}{2} = \frac{10}{B} \quad \Rightarrow \quad B = 5$

Now use $P = A - 5Q$: $20 = A - 5 \cdot 2 \quad \Rightarrow \quad A = 30$

The inverse demand curve is: $P = 30 - 5Q$

Key insight: A single point $(P,Q)$ plus the local elasticity is enough to determine the entire linear demand curve.

Factors Affecting Price Elasticity of Demand

The lecture identifies five determinants:

Factor	Explanation	Examples
Availability of close substitutes	More and closer substitutes → more elastic	Humira (patented drug, no substitutes → inelastic) vs. Crocin (many paracetamol brands → elastic)
Necessity vs. luxury	Necessities inelastic, luxuries elastic	Rice (Ed=0.5) vs. Mountain Dew (Ed=4.4); cigarettes (inelastic); luxury handbags
Narrowness of definition	More narrowly defined → more elastic	Organic oranges vs. oranges; Samsung Galaxy vs. all smartphones
Budget share	Larger share of income → more elastic	Stapler pins (tiny share → ignore price) vs. car (large share → price sensitive)
Time horizon	Longer run → more elastic (more adjustment possible)	Petrol: short-run inelastic (cannot change car), long-run elastic (shift to EV or public transport)

Exam tip: Memorise these five factors. The most common exam errors are confusing necessity/luxury and confusing short-run/long-run effects.

Key Takeaways

• For a linear inverse demand curve $P = A - BQ$, elasticity at any point is $E_d = \frac{1}{B}\frac{P}{Q} = \frac{A}{BQ} - 1$.
• Elasticity falls as quantity increases along the curve.
• Zones: $Q=0$ (perfectly elastic), $0<Q<A/(2B)$ (elastic), $Q=A/(2B)$ (unitary), $A/(2B)<Q<A/B$ (inelastic), $Q=A/B$ (perfectly inelastic).
• Given one $(P,Q)$ and $E_d$, the full linear demand curve can be found if linearity is assumed.
• Five factors determine elasticity: substitutes, necessity/luxury, narrowness, budget share, time horizon.

Elasticity and Revenue

Price elasticity of demand directly answers a manager’s core question: Will a price hike raise or lower my revenue? This section bridges the elasticity concept to real pricing decisions, using a graphical intuition that becomes a crisp decision rule.

Revenue as a rectangle

Total revenue $R = P \times Q$. On an inverse demand curve, revenue at price $P_1$ is the area of the rectangle with height $P_1$ and width $Q_1$ (area $R$ in the basic diagram). When price changes from $P_1$ to $P_2$, quantity moves from $Q_1$ to $Q_2$ (by the law of demand, $Q_2 < Q_1$). The new revenue $P_2 Q_2$ is a different rectangle.

Decomposing the change: gains and losses

When price rises, two forces act on revenue:

flowchart LR
    A[Price ↑] --> B[Gain: sell remaining units at higher price]
    A --> C[Loss: sell fewer units at old price]
    B & C --> D{Net effect on revenue}

Let:

• Area A = $(P_2 - P_1) \times Q_2$ — the extra revenue from selling $Q_2$ units at the higher price (gain).
• Area B = $(Q_1 - Q_2) \times P_1$ — the revenue lost because $Q_1 - Q_2$ fewer units are sold (loss).
• Old revenue $R_1 = P_1 Q_1 = B + C$
• New revenue $R_2 = P_2 Q_2 = A + C$

The change in revenue is $R_2 - R_1 = A - B$. The common area $C$ cancels.

Key insight: The decision to raise price reduces to comparing the gain rectangle $A$ and the loss rectangle $B$.

The decision rule: elasticity tells you which rectangle is bigger

Whether $A > B$, $A < B$, or $A = B$ depends on the price elasticity of demand at the original operating point $(P_1, Q_1)$.

Demand type	$\lvert \text{PED} \rvert$	What happens	$A$ vs $B$	Revenue effect	Manager’s action
Inelastic	$<1$	$\% \Delta Q$ < $\% \Delta P$ (quantity falls only a little)	$A > B$	Revenue increases	Raise price → pass on cost increase
Elastic	$>1$	$\% \Delta Q$ > $\% \Delta P$ (quantity falls a lot)	$B > A$	Revenue decreases	Do NOT raise price; absorb the cost
Unitary elastic	$=1$	$\% \Delta Q$ = $\% \Delta P$	$A = B$	Revenue unchanged	Either action yields same revenue (rare in practice)

Graphically:

• Inelastic demand → steep demand curve; $A$ visibly larger than $B$.
• Elastic demand → flat demand curve; $B$ dominates.

Exam tip: The single most-tested result: Raising price increases total revenue only when demand is inelastic at the current point. The converse: cutting price increases revenue only when demand is elastic.

Worked example: Gurugram Metro

Demand: $Q = 30 - 3P$ (thousands of km travelled)
Inverse demand: $P = 10 - \frac{Q}{3}$ (so $A=10$, $B=1/3$ in $P = A - BQ$ format).
Operating cost rising → COO considers a price increase.

Price elasticity formula for a linear demand:
$\lvert \text{PED} \rvert = \frac{1}{B} \cdot \frac{P}{Q}$

Scenario 1: current price ₹8 per km

• $Q = 30 - 3\times 8 = 6$
• $\lvert \text{PED} \rvert = \frac{1}{1/3} \cdot \frac{8}{6} = 3 \times \frac{4}{3} = 4$
• Since $4 > 1$, demand is elastic.
• Advice: Do NOT raise price – revenue would fall.

Scenario 2: current price ₹4 per km

• $Q = 30 - 3\times 4 = 18$
• $\lvert \text{PED} \rvert = 3 \cdot \frac{4}{18} = 3 \times \frac{2}{9} = \frac{2}{3} \approx 0.67$
• Since $0.67 < 1$, demand is inelastic.
• Advice: Raise price – revenue will increase.

Key takeaways

• Revenue change from a price change = gain rectangle $(P_2-P_1)Q_2$ minus loss rectangle $(Q_1-Q_2)P_1$.
• The comparison of these rectangles is governed by price elasticity at the initial point.
• Inelastic → price and revenue move together; elastic → price and revenue move opposite.
• Unitary elasticity is a theoretical knife-edge; real decisions involve elastic or inelastic ranges.
• Always compute $\lvert \text{PED} \rvert$ at the current operating point before recommending a price change for revenue maximisation.

Income Elasticity of Demand

Income elasticity of demand ($E_I$) measures how responsive quantity demanded is to a change in consumer income, holding all other determinants constant.

$E_I = \frac{\%\,\Delta Q}{\%\,\Delta I} = \frac{(Q_2 - Q_1)/Q_1}{(I_2 - I_1)/I_1}$

• Normal goods: $E_I > 0$ — income increase raises quantity demanded.
• Inferior goods: $E_I < 0$ — income increase reduces quantity demanded.

Exam tip: The sign of income elasticity directly classifies a good as normal or inferior. No extra steps.

Cross Price Elasticity of Demand

Cross price elasticity of demand ($E_{XY}$) measures how responsive the quantity demanded of good $X$ is to a change in the price of good $Y$, holding all other determinants of demand for $X$ constant.

$E_{XY} = \frac{\%\,\Delta Q_X}{\%\,\Delta P_Y} = \frac{(Q_{X2} - Q_{X1})/Q_{X1}}{(P_{Y2} - P_{Y1})/P_{Y1}}$

• Substitutes: $E_{XY} > 0$ (e.g., tea and coffee). A rise in $P_Y$ increases $Q_X$.
• Complements: $E_{XY} < 0$ (e.g., petrol and petrol cars). A rise in $P_Y$ decreases $Q_X$.

Exam tip: Substitutes → positive cross elasticity; complements → negative cross elasticity.

Worked example

You run a grocery store. The price of recreation is expected to increase by 15%. The table below gives cross-price elasticities between selected categories.

Categories	Cross price elasticity
Transportation & recreation	–0.05
Food & recreation	0.15
Clothing & food	–0.18

To find the effect on food sales:

$\frac{\%\,\Delta Q_F}{\%\,\Delta P_R} = 0.15 \quad\Rightarrow\quad \%\,\Delta Q_F = 0.15 \times 15\% = 2.25\%$

Food demand rises by 2.25%, confirming that food and recreation are substitutes.

Price Elasticity of Supply

Price elasticity of supply ($E_S$) measures how responsive quantity supplied is to a change in the selling price of the good, holding all other determinants of supply constant.

$E_S = \frac{\%\,\Delta Q_S}{\%\,\Delta P}$

• Larger $E_S$ → more sensitive supply.
• Examples: a 2% price rise with a 16% quantity increase gives $E_S = 8$; with a 1% quantity increase gives $E_S = 0.5$.

Factors affecting supply elasticity

Factor	Effect on $E_S$
Flexibility of production	More flexible (e.g., multiple substitute inputs) → higher elasticity. Inflexible (e.g., patented medicine with rigid processes) → lower elasticity.
Time frame	Long run → higher elasticity (all inputs variable). Short run → lower elasticity (fixed constraints).

Supply curve shapes and elasticity

Curve shape	$E_S$	Description
Vertical	$0$ (perfectly inelastic)	Quantity supplied does not change with price.
Steep (but not vertical)	$0 < E_S < 1$ (inelastic)	$\% \Delta Q_S < \% \Delta P$
45° line through origin	$1$ (unit elastic)	$\% \Delta Q_S = \% \Delta P$
Flat	$E_S > 1$ (elastic)	$\% \Delta Q_S > \% \Delta P$
Horizontal	$\infty$ (perfectly elastic)	Any price rise above the current price reduces quantity supplied to zero.

Exam tip: Elasticity of supply changes along a typical upward-sloping supply curve — it is larger at lower quantities and smaller at higher quantities (due to capacity constraints).

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Key takeaways

• Income elasticity: positive for normal goods, negative for inferior goods.
• Cross price elasticity: positive for substitutes, negative for complements.
• Price elasticity of supply: driven by production flexibility and time horizon.
• Supply curve shapes: vertical (perfectly inelastic), steep (inelastic), 45° line (unit elastic), flat (elastic), horizontal (perfectly elastic).
• Elasticity of supply varies along the curve, generally decreasing at higher output levels.

Tax Incidence

When a government imposes a specific tax (a fixed amount per unit), it drives a wedge between the price buyers pay ($P_b$) and the price sellers receive ($P_s$). The key insight: the side of the market that is more inelastic bears a larger share of the tax, regardless of whether the tax is legally levied on sellers or buyers. The tax also reduces the quantity traded, creates government revenue, and generates a deadweight loss.

Specific Tax on Sellers: The Wedge

A specific tax of $t$ rupees per unit is imposed on sellers. In equilibrium:

$P_b - P_s = t$

The supply curve in terms of $P_b$ shifts vertically upward by exactly $t$. The demand curve (already in $P_b$) stays unchanged.

For linear inverse demand and supply:

• Demand: $P_b = a - b Q$ (buyers’ price)
• Supply (before tax): $P_s = c + d Q$ (sellers’ price)
• After tax, supply in terms of $P_b$: $P_b = c + t + d Q$

New Equilibrium

Solve $P_b = a - b Q = c + t + d Q$.

$Q_{\text{new}} = \frac{a - c - t}{b + d} = Q^* - \frac{t}{b + d}$

$P_b = \frac{ad + bc + b t}{b + d} = P^* + \frac{b}{b+d}\,t$

$P_s = P_b - t = \frac{ad + bc - d t}{b + d} = P^* - \frac{d}{b+d}\,t$

Where $P^*$ and $Q^*$ are the no‑tax equilibrium.

Variable	After tax	Change from $P^*$ / $Q^*$
$P_b$ (buyers pay)	higher	$+\frac{b}{b+d}\,t$
$P_s$ (sellers receive)	lower	$-\frac{d}{b+d}\,t$
$Q$	lower	$-\frac{t}{b+d}$
Government revenue	$t \cdot Q_{\text{new}}$	–

Exam tip: The formulas for $P_b$, $P_s$, and $Q_{\text{new}}$ are derived by equating quantity demanded and supplied after shifting the supply curve up by $t$. The split between $P_b$ and $P_s$ depends only on the slopes $b$ (absolute slope of demand) and $d$ (slope of supply).

Tax Incidence Depends on Elasticities

The consumer burden (share of $t$ paid by buyers) is:

$\text{Consumer burden} = \frac{P_b - P^*}{t} = \frac{b}{b+d}$

The producer burden is $\frac{d}{b+d}$.

Multiply numerator and denominator by $\frac{Q^*}{P^*}$ to convert slopes into elasticities:

$\frac{b}{b+d} \; \Rightarrow \; \frac{ \frac{1}{\epsilon_d} }{ \frac{1}{\epsilon_d} + \frac{1}{\epsilon_s} } = \frac{\epsilon_s}{\epsilon_s + \epsilon_d}$

where $\epsilon_d$ is price elasticity of demand and $\epsilon_s$ is price elasticity of supply (both evaluated at the no‑tax equilibrium).

Condition	Which side bears more tax?	Intuition
$\epsilon_s > \epsilon_d$ (supply more elastic)	Consumers bear more	Inelastic demand cannot adjust; sellers pass on tax
$\epsilon_s < \epsilon_d$ (demand more elastic)	Producers bear more	Inelastic supply absorbs the tax
$\epsilon_s = \epsilon_d$	Equal burden	Symmetric response

Key rule: The more inelastic side bears the larger burden.

Example: Luxury Tax on Yachts

Yachts are luxury goods with highly elastic demand (many substitutes). Supply (shipbuilding) is relatively inelastic. Therefore, when a specific tax is imposed on yacht sales, producers bear most of the burden – the price buyers pay rises only slightly, while the price sellers receive falls substantially.

Exam tip: Do not assume that taxing sellers always hurts sellers more. The legal incidence (who writes the cheque) is irrelevant; the economic incidence depends solely on relative elasticities.

Deadweight Loss (DWL)

The tax reduces quantity from $Q^*$ to $Q_{\text{new}}$. The lost surplus (consumer + producer) that is not transferred to government revenue is the deadweight loss – a pure efficiency loss.

With linear curves:

$\text{DWL} = \frac{1}{2}\,t\,(Q^* - Q_{\text{new}}) = \frac{1}{2}\,t \cdot \frac{t}{b+d} = \frac{t^2}{2(b+d)}$

In elasticity terms:

$\text{DWL} = \frac{1}{2}\,t^2 \cdot \frac{Q^*}{P^*} \cdot \frac{1}{\frac{1}{\epsilon_d} + \frac{1}{\epsilon_s}}$

As either $\epsilon_d$ or $\epsilon_s$ increases, DWL increases. More elastic curves mean a larger quantity reduction for a given tax, hence a larger deadweight loss.

Surplus Flows Diagram

flowchart TD
    subgraph Before tax
        A["`**Consumer surplus** = C + R + A`"]
        B["`**Producer surplus** = L + B + P`"]
        G["`**Government revenue** = 0`"]
        Total["`**Total surplus** = C + R + A + L + B + P`"]
    end
    subgraph After tax
        A2["`**Consumer surplus** = C`"]
        B2["`**Producer surplus** = P`"]
        G2["`**Government revenue** = R + L`"]
        DWL["`**Deadweight loss** = A + B`"]
        Total2["`**Total surplus** = C + P + R + L`"]
    end

• Areas $R$ and $L$ are transferred from consumers and producers to the government.
• Areas $A$ and $B$ are lost – the deadweight loss.

Tax on Buyers (Equivalent)

Imposing the same specific tax on buyers (e.g., a sales tax) shifts the demand curve downward by $t$ instead of shifting supply upward. The final equilibrium $P_b$, $P_s$, $Q_{\text{new}}$, and the incidence are identical. The legal designation does not matter.

Price Caps and Price Floors (brief)

Governments sometimes intervene with price controls, which also create surpluses or shortages and deadweight loss.

Price Ceiling (Cap)

• Legally maximum price $P_c$.
• Effective only if $P_c < P^*$ → excess demand (shortage).
• Transfers surplus from producers to consumers, but causes rationing and DWL.

Price Floor (Minimum)

• Legally minimum price $P_f$.
• Effective only if $P_f > P^*$ → excess supply (surplus).
• Protects sellers (e.g., agricultural price supports) but creates wasted output and DWL.

Exam tip: An ineffective price control (above equilibrium for ceiling, below for floor) has no effect on the market.

Key takeaways

• A specific tax creates a wedge $P_b - P_s = t$; the supply curve shifts up by $t$ in terms of $P_b$.
• The side with more inelastic demand or supply bears a larger share of the tax.
• Linear formulas: $P_b = P^* + \frac{b}{b+d}t$, $P_s = P^* - \frac{d}{b+d}t$, $Q = Q^* - \frac{t}{b+d}$.
• Deadweight loss = $\frac{t^2}{2(b+d)}$; increases with elasticities.
• Tax incidence is independent of who legally pays the tax.
• Price controls (caps and floors) cause shortages/surpluses and DWL when effective.