Chapter 1 Markets Intermediate Microeconomics: © 2016 Samiran Banerjee A Tool-Building Approach Routledge, UK © 2016 Samiran Banerjee

IIndependent variable Market Demand Market demand: Qd = f(p) Example: Qd = 120 – 2p Inverse market demand: p = g(Qd) Example: p = 60 – 0.5Qd *The function g is the inverse of f. IDependent variable IIndependent variable Vertical intercept Slope

Adding inverse demands Suppose the inverse demand on market 1 is p = 40 – 2Q1d

Adding inverse demands Suppose the inverse demand on market 2 is p = 30 – Q2d

Adding inverse demands Graphically, add the two market demands horizontally! • If p ≥ $30, only consumers in market 1 buy • If p < $30, consumers in both markets buy

Adding inverse demands To derive the inverse demand mathematically: • “Flip” p = 40 – 2Q1d to get Q1d = 20 – 0.5p • “Flip” p = 30 – Q2d to get Q2d = 30 – p • Add them: Qd = Q1d + Q2d = 50 – 1.5p • “Flip” to obtain the inverse aggregate demand: p = 100/3 – 2Qd/3 “FLIP, FLIP, ADD, and FLIP!”

Market Supply Suppose the inverse supply is p = Qs

Market Equilibrium • Set the inverse aggregate demand equal to the inverse supply: 100/3 – 2Qd/3 = Qs • Since Qd = Qs = Q* in equilibrium, Q* = 20 • Then p*= $20

Market Stability • Dynamic story • What happens if p > p*

Market Welfare • Consumer surplus: value to buyer minus price paid • Producer surplus: price received minus value to seller

Demand Determinants ◊ increase in demand: ◊ decrease in demand: • Income of buyers ◊ increase in demand: ◊ decrease in demand: • Prices of other goods • Tastes or preferences of buyers • Number of buyers

Supply Determinants • Prices of inputs • Technology • Number of sellers

Intervention: Price ceiling • Set a maximum price below p* • Smaller of the quantities demanded or supplied is traded

Price ceiling: Welfare • A = (largest possible) consumer surplus • B = producer surplus • C = (smallest possible) deadweight loss Of all the possible buyers from zero to Q_bar, we don’t know who actually purchases. If those who value it the most purchase, then A represents the maximum possible consumer surplus. It could well be lower. Consequently, the deadweight loss could be much higher.

Intervention: Price floor • Set a minimum price above p* • Smaller of the quantities demanded or supplied is traded

Price floor: Welfare • A = consumer surplus • B = (largest possible) producer surplus • C = (smallest possible) deadweight loss Of all the possible seller from zero to Q_tilde, we don’t know who actually sells. If those who have the lowest reservation price sell, then B represents the maximum possible consumer surplus. It could well be lower. Consequently, the deadweight loss could be much higher.

Intervention: Quota • Set a maximum quantity below Q* • The supply curve becomes vertical at the quota

Quota: Welfare • A = consumer surplus • B = producer surplus • C = deadweight loss

Intervention: Per unit tax • A per unit tax of t dollars is imposed on sellers • The new inverse supply is pn = po + t • Buyers pay pn* to buy one unit • Sellers receive pn* – t from each sale

Per unit tax: Welfare • A = consumer surplus • B = producer surplus • T = tax revenue • C = deadweight loss

Per unit tax: Sellers vs. buyers On sellers On buyers • New inverse supply is pn = po + t • pn* is price paid by buyers • New inverse demand is pn = po – t • pn* is price received by sellers When a tax is on sellers, the market equilibrium price shows the price including the tax. When a tax is on buyers, the market equilibrium price shows the price paid by buyers before they have paid the tax.

Intervention: Per unit subsidy • A per unit subsidy of s dollars is given to sellers • The new inverse supply is pn = po – s • Buyers pay pn* to buy one unit • Sellers receive pn* + s from each sale

Per unit subsidy: Welfare • A = consumer surplus • B = producer surplus • Green parallelogram = subsidy payment • C = deadweight loss The height of the parallelogram is the per-unit subsidy. Multiplying it by the length from zero to Q_n* gives us the total subsidy payment which is the area.

Demand elasticities Demand elasticities measure how the quantity demanded of a product changes with different determinants of demand. In general, Percentage change in qty. demanded of x Elasticity = Percentage change in determinant “epsilon” • Own-price elasticity of demand, εxx: determinant = px • Cross-price elasticity of demand, εxy: determinant = py • Income elasticity of demand, ηx: determinant = income “eta”

Own-price elasticity . • Given two points on an inverse market demand: (Qo, po) and (Qn, pn) • The percentage change in quantity is [(Qn – Qo)/Qo] x 100 = (ΔQ/Qo) x 100 • The percentage change in price is [(pn – po)/po] x 100 = (Δp/po) x 100 ΔQ Δp po Qo . ε = = ∂Q ∂p Derivative of market demand at original point* ~ * For infinitesimal price changes

Own-price elasticity: linear demand OF ε @ B = ∂Q ∂p po Qo . (Qo, po) OE = FB FB/FA ε @ B = OF FA

Other demand elasticities • The cross price-elasticity for good x with respect to the price of y is • The income elasticity for good x is . ∂Qx ∂py py Qx εxy = ∂Qx ∂m m Qx . ηx =

Supply elasticity The supply elasticity measures how the quantity supplied of a product changes with the price of the product. In general, εs = ∂Qs ∂p po Qo . s