Term 2 · Module 1 of 4

Forces of Demand and Supply

Principles of Microeconomics

Introduction and Course Overview

Microeconomics studies the decision-making of individual households and firms in the presence of scarcity – limited resources relative to unlimited wants. This module introduces the foundational concepts needed to analyze trade-offs faced by consumers and firms, and builds the language of economics.

Course Objectives

  1. Learn economic concepts for better decision-making.
  2. Interpret real-world problems through an economic lens.
  3. Master the glossary and language of economics – read newspapers like Live Mint or The Economist to apply concepts to current events.

Scope: Microeconomics vs. Macroeconomics

FieldFocusExamples
MicroeconomicsDecisions of households, firms, and individual marketsHow much to consume vs. save; input allocation; pricing and output decisions
MacroeconomicsDecisions of the economy as a whole or the governmentMeasuring national income; growth; distributing subsidies; welfare spending

Exam tip: Remember that both fields study decision-making under scarcity – the difference is the unit of analysis (individual vs. aggregate).

Economic Models: Maps of Reality

Models are mathematical representations of variables that abstract away from details to focus on the key forces.

  • Example: Quantity produced Q=f(K,L)Q = f(K, L) where KK = capital, LL = labour.
  • Models always omit some variables – the choice of what to include depends on the question.
  • Analogy: A map for a month-long road trip includes highways and cities; a map for a day trip near home includes local streets. The level of detail differs because the task differs.

Key insight: Models are always wrong in the sense of incomplete, but they bring discipline to thinking and highlight the major forces.

Course Outline (Four Modules)

ModuleTopics
Module 1 – Basics & Forces of Demand and SupplyOpportunity cost, sunk cost, marginal principle; demand and supply model; factors affecting demand and supply
Module 2 – Market Equilibrium & ElasticityEquilibrium; elasticity of demand/supply; tax incidence; price floors and ceilings; equity vs. efficiency
Module 3 – The FirmCost categories; profit maximization; supply curves in perfect competition
Module 4 – MonopolyMonopolist pricing/quantity; social costs of monopoly; price discrimination

Key resource: Principles of Microeconomics by N. Gregory Mankiw.

Key takeaways

  • Microeconomics = household/firm decisions; macroeconomics = economy-wide decisions.
  • Economic models are simplified representations that omit details to focus on the question.
  • All models are incomplete (“wrong”) but useful when the right variables are chosen.
  • The course builds from basic principles (opportunity cost, sunk cost, marginal thinking) through demand/supply, elasticity, firm behavior, and market structures.

The GM Coupon Case: Economic Value vs. Nominal Value

In 1993, GM faced a class-action lawsuit over alleged design flaws in its third-generation light trucks (1973–1991). NHTSA pushed for a recall of over 4 million trucks. To settle without admitting liability, GM offered each affected owner a 1,000coupon∗∗towardanewGMlighttruck.Thecouponcouldbe∗∗transferred∗∗toathirdparty,whowouldthenreceiveonlya∗∗1,000 coupon** toward a new GM light truck. The coupon could be **transferred** to a third party, who would then receive only a **500 discount. Coupons were valid for 15 months; only one per purchase.

Media estimated the settlement cost at **4.7billion∗∗(4.7millioncoupons×4.7 billion** (4.7 million coupons × 1,000). The judge rejected the settlement, suspecting the actual value to owners was far lower. Economic reasoning confirms the suspicion.

Actual value depends on how coupons are used

Only 0.6 million of the 4.7 million coupon holders were expected to buy a new GM light truck themselves. Their direct benefit:

0.6M×$1,000=$600M0.6\text{M} \times \$1,000 = \$600\text{M}

The remaining 4.1 million holders would try to transfer (sell) their coupons. But only 1.4 million first-time buyers were willing to buy a coupon. Because each transferred coupon gives only **500∗∗discount,abuyerwillpayatmost500** discount, a buyer will pay at most 500. With 4.1 million sellers and 1.4 million buyers, the market price for a coupon is driven very low — estimated at $20 per coupon.

Value from transfers:

1.4M×$20=$28M1.4\text{M} \times \$20 = \$28\text{M}

Total actual value to affected owners

$600M+$28M=$628M(not $4.7B)\$600\text{M} + \$28\text{M} = \$628\text{M} \quad (\text{not } \$4.7\text{B})

The superficial calculation ignored the forces of demand and supply — limited number of buyers relative to sellers created a glut, collapsing the coupon price. This case illustrates the gap between nominal generosity and real economic value.

Exam tip: When a good is transferable and supply exceeds demand, its market price can fall far below face value. Always consider who the buyers are and how many can actually use the transfer.

Scarcity, Trade-offs, and Economic Decision-Making

The GM example reveals a deeper theme: scarcity — limited resources vs. unlimited wants. Economists study trade-offs that arise from scarcity.

Two common managerial decisions illustrating scarcity and trade-offs:

  1. Semiconductor shortage (2021–2023): Car makers had to decide how to distribute limited microcontrollers across car models.
  2. Advertising budget allocation: With a fixed budget, more ads for Model A means less for Model B.

Both involve infinite wants (desire more microcontrollers, more ads) but limited resources → must choose → trade-off: having more of one thing means having less of another.

Two prevalent trade-offs in real life:

  • Consumption vs. saving: Individuals decide how much income to spend now vs. save for future consumption.
  • Efficiency vs. equity:
    • Efficiency means getting the largest possible output from scarce resources (e.g., a car that goes 20 km on 2 liters is more efficient than one that goes 15 km on the same fuel).
    • Equity concerns how fairly the economic gains are distributed (e.g., equal cake slices vs. one person getting 70%).

Often, these goals conflict. For example, government programs to reduce inequality (equity) — such as employment guarantees or free healthcare — require taxing the rich or businesses. Higher taxes may reduce incentives to work and produce, lowering overall efficiency.

Exam tip: The efficiency–equity trade-off is a foundational tension in public policy. Remember: policies that redistribute income can reduce the size of the pie (efficiency) even as they divide it more equally (equity).

Key takeaways

  • Economic value ≠ nominal value. The GM coupon settlement appeared worth 4.7Bbutactualvaluewas 4.7B but actual value was ~630M because only a fraction of coupons could be used (demand for transfers was much smaller than supply).
  • Scarcity forces trade-offs: limited resources + unlimited wants → choices.
  • Trade-offs exist at every level — firms, consumers, governments.
  • Efficiency = getting the most from scarce inputs; Equity = fairness in distribution.
  • Increasing equity (e.g., through taxes) can reduce efficiency by dampening incentives.

Conceptual Tools of an Economist: Opportunity Costs and Sunk Costs

Sound economic decision-making rests on three fundamental concepts: opportunity cost, sunk cost, and the marginal principle. This section covers the first two; marginal analysis is introduced separately.


Opportunity Cost

Intuition: Every choice has a trade-off. The true cost of picking one option is the value of the next best alternative you give up. Most people only count out‑of‑pocket expenses and miss this hidden cost, leading to overestimated benefits and poor decisions.

Formal Definition

Opportunity cost is the value of the next best alternative that must be forgone as a result of a decision.

It is typically implicit—not recorded in any ledger—and varies from person to person.

Example: Enrolling in an Online BBA

BenefitsCosts
Learning new concepts, tools, and perspectivesTuition fee, books
Increased future earningsMental discomfort of learning
Opportunity cost: time spent studying (could have been used for part‑time work, family, or other degrees)

The opportunity cost is often the value of the foregone alternative, e.g., the income from a part‑time job or the utility from time with family. Because it is not a visible expense, it is easily ignored—thinking like an economist means always including it.

Real‑World Application: Qantas “Flight to Nowhere” (September 2020)

During the COVID‑19 pandemic, Qantas operated a 7‑hour scenic flight that sold out in 10 minutes at prices from 600to600 to 2,500. The flight flew over Uluru and the Great Barrier Reef and returned to the same airport.

Why did affluent passengers pay a premium? The opportunity cost of their disposable income was very low—they could not spend it on foreign travel, resorts, or weekend getaways. With few alternative uses, spending $2,500 on a flight seemed reasonable. Post‑pandemic, the same money has many high‑value uses (overseas trips, vacations), so the opportunity cost is higher. A similar flight today would likely not sell out at such prices.

Exam tip: Opportunity cost changes with context. When alternatives are scarce, the opportunity cost is low; when many attractive alternatives exist, it is high.

Key takeaways – Opportunity Cost

  • It is the value of the next best alternative forgone.
  • It is implicit and often overlooked, causing overestimation of net benefits.
  • It differs across individuals (money vs. time vs. utility).
  • Always include opportunity cost in any cost‑benefit analysis.

Sunk Cost

Intuition: Sunk costs are expenses already incurred that cannot be recovered. They are in the past and should never influence a forward‑looking decision. Yet people cling to them—this is the sunk cost fallacy.

Formal Definition

Sunk costs are costs that are beyond recovery at the moment a decision is being made.

Example: The Movie That Should Have Been Walked Out Of

You buy a costly ticket for a movie. After 30 minutes, it is clearly terrible. Most people stay, thinking, “I paid for it—I might as well watch it.” This is the sunk cost fallacy. The ticket money is already spent and unrecoverable; sitting through the movie only adds suffering (an additional cost) to the already lost money. The rational decision is to leave.

Worked Example: Bus vs. Car to Goa

You are in Bangalore and want to travel to Goa (600 km). Options:

  • Bus: ₹1,500.
  • Your own car.

Annual costs of car ownership (10,000 km/year):

Cost itemAnnual amount (₹)
Insurance30,000
Interest payments10,000
Fuel and oil20,000
Maintenance2,000
Total62,000

Naïve calculation (including all costs): Cost per km = Rs. 62,000÷10,000 km=Rs. 6.2/km\text{Rs. }62,000 \div 10,000 \text{ km} = \text{Rs. }6.2/\text{km} Trip cost (600 km) = 600×Rs. 6.2=Rs. 3,720600 \times \text{Rs. }6.2 = \text{Rs. }3,720 Conclusion: Bus (₹1,500) is cheaper → take the bus.

Correct calculation (ignore sunk costs): Insurance and interest are sunk—paid upfront and unaffected by how many km you drive. Only variable costs (fuel, oil, maintenance) matter for the trip.

Variable cost per year = ₹20,000 + ₹2,000 = ₹22,000 Variable cost per km = Rs. 22,000÷10,000 km=Rs. 2.2/km\text{Rs. }22,000 \div 10,000 \text{ km} = \text{Rs. }2.2/\text{km} Trip cost (600 km) = 600×Rs. 2.2=Rs. 1,320600 \times \text{Rs. }2.2 = \text{Rs. }1,320 Conclusion: Car (₹1,320) is cheaper than bus (₹1,500) → take the car.

Key lesson: Sunk costs (insurance, interest) must be ignored when comparing marginal trip costs. Failing to do so leads to the wrong decision.

Exam tip: In any “build vs. buy” or “continue vs. stop” decision, identify sunk costs first. Only future, avoidable costs matter. The sunk cost fallacy is one of the most common reasoning errors tested.

Key takeaways – Sunk Cost

  • A cost already incurred and unrecoverable.
  • Ignore sunk costs when making any forward‑looking decision.
  • The sunk cost fallacy: acting as if watching a bad movie or finishing a failing project “recovers” the money already spent.
  • Always separate sunk (fixed, past) from variable (future, avoidable) costs.

Marginal Principle

The marginal principle is a heuristic for net benefit maximization. Economic agents — consumers and firms — constantly face choices about “how much” of an activity to do. The principle guides them to the quantity that maximizes the difference between total benefits and total costs.

Core idea: think in increments

  • Marginal benefit (MB): the change in total benefit from carrying out one additional unit of an activity. For a consumer: the extra utility from one more glass of juice. For a firm: the extra revenue from selling one more unit (marginal revenue).

  • Marginal cost (MC): the change in total cost from carrying out one additional unit of an activity. For a consumer: the price of that extra unit (marginal price). For a firm: the cost of producing one more unit.

Formally, for a discrete change of 11 unit:

MB=ΔTotal Benefit,MC=ΔTotal Cost\text{MB} = \Delta \text{Total Benefit}, \quad \text{MC} = \Delta \text{Total Cost}

The decision rule

As long as MB≥MC\text{MB} \geq \text{MC}, net benefit increases. Keep doing the activity. Stop when MC>MB\text{MC} > \text{MB}.

AgentNet benefit (maximand)Condition to continue doing one more unit
ConsumerNet utility = Total utility – Total priceMarginal utility ≥\geq Marginal price
FirmProfit = Total revenue – Total costMarginal revenue ≥\geq Marginal cost

The rule applies step by step — each additional unit is evaluated independently.


Worked example: Rahul’s bookstores

Rahul runs a chain in Bangalore. He currently has 3 stores and is deciding whether to open a 4th. His goal: maximise total profit.

Total revenue (TR) and total cost (TC) by number of stores:

Number of storesTR (₹)TC (₹)Profit (₹)
12,00,0001,00,0001,00,000
23,60,0002,00,0001,60,000
35,10,0003,00,0002,10,000
45,60,0004,00,0001,60,000

Profit is maximised at 3 stores (₹2,10,000). Opening the 4th store reduces profit.

The trap: averaging instead of marginalising

Rahul might calculate average benefit (TR/number of stores) and average cost (TC/number of stores):

StoresAvg. benefit (₹)Avg. cost (₹)
12,00,0001,00,000
21,80,0001,00,000
31,70,0001,00,000
41,40,0001,00,000

At 4 stores, average benefit (₹1,40,000) > average cost (₹1,00,000) — suggesting positive “average profit”. Yet total profit fell. Why? Averages hide what the last store contributes.

The correct marginal analysis

Compute marginal benefit (change in TR) and marginal cost (change in TC) for each additional store:

Store numberMB (₹)MC (₹)Decision
1st2,00,0001,00,000MB > MC → open
2nd1,60,0001,00,000MB > MC → open
3rd1,50,0001,00,000MB > MC → open
4th50,0001,00,000MC > MB → do not open
  • MC is constant at ₹1,00,000 per store.
  • MB falls: the 4th store contributes only ₹50,000 revenue but costs ₹1,00,000.
  • Total profit decreases by ₹50,000 when the 4th store is added (from ₹2,10,000 to ₹1,60,000).

Exam tip: Always use marginal (incremental) analysis when deciding whether to change the level of an activity. Comparing averages is a common mistake — it can recommend actions that lower total net benefit.


Marginal principle in life decisions

The same logic applies beyond business. The decision to get married can be framed as:

  • Marginal benefit of continued search: the expected gain in utility from waiting another year to find a better-matched partner.
  • Marginal cost of continued search: the loneliness and opportunity cost of delaying marriage.

When MB of searching falls to equal MC, the optimal point is reached — time to propose.


Key takeaways

  • The marginal principle: keep doing an activity as long as MB≥MC\text{MB} \geq \text{MC}; stop when MC>MB\text{MC} > \text{MB}.
  • Net benefit = total benefit – total cost; maximising net benefit is the goal.
  • Marginal values (change from one extra unit) drive the decision, not averages.
  • Consumers apply it via marginal utility vs. price; firms via marginal revenue vs. marginal cost.
  • The principle is universal: any incremental decision — from opening stores to marriage — can be analysed this way.

1. Markets and Perfect Competition

A market exists wherever buyers and sellers exchange money for a good or service. Markets differ in the number and size of sellers.

  • Many small sellers – e.g., mango vendors, cab drivers.
  • Few large sellers – e.g., satellite launch providers (India, USA, Russia, China) → oligopolistic market.
  • Single seller – e.g., Humira (arthritis drug) sold only by AbbVie from 2002–2016 → monopoly market.

Perfectly Competitive Markets

A market is perfectly competitive when two conditions hold:

  1. The goods offered for sale are identical.
  2. Buyers and sellers are so numerous that no single one can influence the price.

Exam tip: Most real markets are not perfectly competitive, but the demand‑and‑supply model still gives powerful insights wherever goods are nearly identical and entry is free. This model is the “heart of economics.”

Key takeaways

  • Markets are defined by buyers and sellers exchanging money for goods/services.
  • Oligopoly: few large sellers; monopoly: one seller; perfect competition: many small sellers.
  • Perfect competition requires identical goods and many price‑taking agents.
  • The model of demand and supply is built on the perfectly competitive market.

2. Demand: The Law and Its Determinants

Quantity demanded is the amount buyers are willing and able to purchase at a given price. Wanting alone is not enough – ability (income) is required.

Demand Schedule and Demand Curve

  • Demand schedule: a table showing quantity demanded at different prices, holding all other influences constant.
  • Demand curve: the graph of the demand schedule (price on y‑axis, quantity on x‑axis). It slopes downward.

Example – Jay’s mangoes:

Price (₹/dozen)Quantity demanded (dozens/month)
012
10010
2008
……
7000

The Law of Demand

As the price of a good increases, the quantity demanded decreases (ceteris paribus). This inverse relationship holds for nearly all goods and services.

Market Demand

Market demand = sum of individual demands at each price. Example – Jay + Vijay:

Price (₹/dozen)Jay’s QdVijay’s QdMarket Qd
012719
10010616
…………

The market demand curve is the horizontal sum of individual demand curves.

Movement Along vs. Shift of the Demand Curve

  • Movement along the demand curve – caused only by a change in the good’s own price.
  • Shift of the demand curve – caused by a change in any other determinant (shifters).
    • Rightward shift = increase in demand (more bought at every price).
    • Leftward shift = decrease in demand.

Determinants of Demand (Shifters)

ShifterDescriptionExampleDirection of shift
IncomeNormal good: income ↑ → demand ↑. Inferior good: income ↑ → demand ↓.Refined oil → cold‑pressed oil when income rises (inferior).Normal: right when income ↑; Inferior: left when income ↑
Price of related goods – Substitutes↑ price of substitute → ↑ demand for the good.Tea & coffee; mangoes & lychees.Right when substitute’s price ↑
Price of related goods – Complements↑ price of complement → ↓ demand for the good.Video game consoles & games; petrol cars & petrol.Left when complement’s price ↑
PreferencesTastes change due to trends, health, celebrity influence.M.S. Dhoni playing Candy Crush → 3 million downloads in 3 hours.Right if preference strengthens
Expectations of future pricesExpect higher future price → buy more now.Lockdown announcement → hand‑sanitizer sales soared.Right if future price expected to rise
Number of buyersMore buyers → greater market demand.Pandemic increased buyers of disposable gloves.Right with more buyers

Exam tip: Know the difference between a movement along the curve (price change) and a shift (any other factor). The most common mistake is confusing a quantity change due to price with a change in demand.

Key takeaways

  • Quantity demanded is willingness + ability; it falls as price rises (Law of Demand).
  • The market demand curve is the horizontal sum of individual demand curves.
  • A change in price causes a movement along the curve; a change in income, preferences, prices of related goods, expectations, or number of buyers causes a shift.
  • Substitutes: price of one ↑ → demand for the other ↑. Complements: price of one ↑ → demand for the other ↓.
  • Normal goods: demand rises with income; inferior goods: demand falls with income.

Law of Supply

Supply is the side of the market that answers: How much are sellers willing and able to offer at a given price? The core intuition is simple — as the price of a good rises, producing it becomes more profitable, so sellers increase output. The law of supply formalises that positive relationship.

Quantity Supplied

Quantity supplied is the amount of a good that sellers are willing and able to sell at a particular price.

Example — Jay the wheat farmer Jay has three plots of land, each capable of growing up to 10 quintals of wheat, but with different costs:

PlotMax output (quintals)Marginal cost per quintal (₹)
A101,000
B101,100
C101,200
  • Marginal cost (MC) is constant on each plot and rises across plots (A → B → C).
  • Marginal benefit (MB) = selling price per quintal.
  • A plot is used only if MB ≥ MC.

Decision rule (marginal thinking): Produce on plot i if P≥MCi\text{Produce on plot } i \text{ if } P \ge MC_i

Applying this rule:

Expected price (₹/quintal)Plots usedQuantity supplied (quintals)
800None0
900None0
1,000A (MB=MC)10
1,100A (profitable), B (MB=MC)20
1,200A, B, C (MB=MC)30

Quantity supplied rises with price.

Exam tip: Marginal cost is the key to a seller’s supply decision. Only produce if price covers the marginal cost of that unit.


Law of Supply

Law of supply: Holding all other factors constant, the quantity supplied of a good increases when its price increases (and decreases when price decreases).

Intuition: Higher prices make it profitable for sellers to bring less efficient (higher-cost) resources into production — e.g., Jay uses poorer plots B and C only when price is high enough.


Supply Schedule and Supply Curve

Supply schedule: A table showing the relationship between the price of a good and the quantity supplied, ceteris paribus (holding everything else constant).

Supply curve: The graphical representation of the supply schedule. By convention, price is on the vertical axis (y) and quantity on the horizontal axis (x).

  • Because of the law of supply, the supply curve slopes upward.
  • A change in price causes a movement along the supply curve (e.g., price ↑ → move up the curve to a higher quantity).

Market Supply

Market supply = sum of the quantities supplied by all sellers at each price.

Example — market with two sellers, Jay and Vijay

Price (₹/quintal)Jay’s QsVijay’s QsMarket Qs
800000
90001010
1,000102030
1,100203050
1,200304070
  • The market supply curve is the horizontal summation of individual supply curves.

Shifts in Supply (Change in Supply)

A change in any factor other than price shifts the entire supply curve.

  • Rightward shift = increase in supply (more supplied at every price).
  • Leftward shift = decrease in supply (less supplied at every price).

Determinants that increase supply (shift right)

FactorExampleMechanism
Technology improvesAdvanced fertilisers → each plot yields 12 quintals instead of 10Lower cost per unit; higher output at same price
Input prices fallCheaper silicon wafers → solar panel supply risesLower production cost
Expected future prices decreaseSeller rushes to sell now before price dropsCurrent supply rises

Determinants that decrease supply (shift left)

FactorExampleMechanism
Technology deterioratesCrop disease reduces yieldHigher effective cost
Input prices riseLabour or fertiliser becomes costlierHigher production cost
Expected future prices increaseSeller hoards today, expecting higher prices tomorrowCurrent supply falls

Exam tip: Movement along the supply curve is caused by a change in the good’s own price. A shift of the curve is caused by a change in technology, input prices, or expectations. Never confuse the two.


Key Takeaways

  • Quantity supplied is the amount sellers are willing and able to sell at a given price.
  • Law of supply: price ↑ → quantity supplied ↑ (ceteris paribus).
  • Supply schedule (table) → supply curve (upward-sloping graph).
  • Market supply = horizontal sum of individual supplies.
  • A change in price causes a movement along the supply curve; a change in technology, input prices, or expectations causes the curve to shift (right = increase, left = decrease).

Practice Problems

Three problems illustrate core microeconomic concepts: opportunity cost, supply functions, and demand functions.

Problem 1: Opportunity Cost of Time

Intuition: When choosing between alternatives, the opportunity cost of a decision is the value of the next best option forgone. Ramesh compares only explicit profit but ignores the value of his time.

Worked example:

  • Option A – Set up own shop: Revenue = ₹70,000, Cost = ₹50,000 → Profit = ₹20,000.
  • Option B – Sell inventory to Suresh + return to handyman: Profit from sale = ₹60,000 – ₹50,000 = ₹10,000. Additional income from handyman work (one month) = ₹15,000. Net benefit = ₹10,000 + ₹15,000 = ₹25,000.

Since ₹25,000 > ₹20,000, Option B is superior. Ramesh’s mistake: he compared only the ₹20,000 vs. ₹10,000, ignoring the opportunity cost of his time (the ₹15,000 he could earn as a handyman). Including that cost reverses the decision.

DecisionExplicit profit (₹)Additional income (₹)Total (₹)
Set up shop20,000020,000
Sell to Suresh + handyman10,00015,00025,000

Exam tip: Always account for opportunity cost – the value of the next best use of resources (here, time). The right comparison is between total benefits, not just visible profits.


Problem 2: Supply Function for HDTVs

The supply function relates quantity supplied (QsxQ_s^x) to price of the good (PXP_X) and other determinants. Given:

Qsx=2000+3PX−4PY−PIQ_s^x = 2000 + 3P_X - 4P_Y - P_I

where PXP_X = price of HDTV, PYP_Y = price of tablets (substitute in production), PIP_I = price of inputs.

(a) Quantity produced at given values

Substitute PX=14000P_X = 14000, PY=10000P_Y = 10000, PI=2000P_I = 2000:

Qsx=2000+3(14000)−4(10000)−2000=2000+42000−40000−2000=2000 units\begin{aligned} Q_s^x &= 2000 + 3(14000) - 4(10000) - 2000 \\[2pt] &= 2000 + 42000 - 40000 - 2000 \\[2pt] &= 2000 \text{ units} \end{aligned}

(b) Supply curve (holding other variables constant)

Treat PXP_X as variable; substitute PY=10000P_Y = 10000, PI=2000P_I = 2000:

Qsx=2000+3PX−4(10000)−2000=3PX−40000Q_s^x = 2000 + 3P_X - 4(10000) - 2000 = 3P_X - 40000

Supply curve: Qsx=3PX−40000Q_s^x = 3P_X - 40000 Inverse supply curve (price as function of quantity):

PX=Qsx+400003P_X = \frac{Q_s^x + 40000}{3}

Problem 3: Demand Function and Demand Curve

The demand function for good X:

Qdx=10200−3PX+4PY−I+0.02AXQ_d^x = 10200 - 3P_X + 4P_Y - I + 0.02A_X

where PXP_X = price of X, PYP_Y = price of related good Y, II = consumer income, AXA_X = advertising expenditure.

(a) Is good X a substitute or complement? Normal or inferior?

  • Cross‑price effect: ∂Qdx∂PY=+4>0\frac{\partial Q_d^x}{\partial P_Y} = +4 > 0 → as PYP_Y rises, QdxQ_d^x increases → X and Y are substitutes.
  • Income effect: ∂Qdx∂I=−1<0\frac{\partial Q_d^x}{\partial I} = -1 < 0 → as income rises, quantity demanded falls → X is an inferior good. Correction: a negative income coefficient indicates an inferior good, not a normal good.

Exam tip: The sign of the cross‑price coefficient directly tells substitutes (+) or complements (−). The sign of the income coefficient tells normal (+) or inferior (−).

(b) Quantity demanded at given values

Given PX=200P_X = 200, PY=150P_Y = 150, I=10000I = 10000, AX=2000A_X = 2000:

Qdx=10200−3(200)+4(150)−10000+0.02(2000)=10200−600+600−10000+40=240 units\begin{aligned} Q_d^x &= 10200 - 3(200) + 4(150) - 10000 + 0.02(2000) \\[2pt] &= 10200 - 600 + 600 - 10000 + 40 \\[2pt] &= 240 \text{ units} \end{aligned}

(c) Demand curve (holding other variables constant)

Substitute PY=150P_Y = 150, I=10000I = 10000, AX=2000A_X = 2000:

Qdx=10200−3PX+4(150)−10000+0.02(2000)=10200−3PX+600−10000+40=840−3PX\begin{aligned} Q_d^x &= 10200 - 3P_X + 4(150) - 10000 + 0.02(2000) \\[2pt] &= 10200 - 3P_X + 600 - 10000 + 40 \\[2pt] &= 840 - 3P_X \end{aligned}

Demand curve: Qdx=840−3PXQ_d^x = 840 - 3P_X Inverse demand curve:

PX=840−Qdx3=280−Qdx3P_X = \frac{840 - Q_d^x}{3} = 280 - \frac{Q_d^x}{3}

Key Takeaways

  • Opportunity cost = value of forgone alternative; always include it when comparing options.
  • A supply curve is derived from the supply function by holding non‑price variables constant.
  • The sign of a cross‑price coefficient in a demand function indicates substitutes (++) or complements (−-); the sign of the income coefficient indicates normal (++) or inferior (−-).
  • Worked examples require plugging given numbers into the function and simplifying step by step.