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

2. 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

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

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

5. 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

6. 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!”

7. Market Supply
Suppose the inverse supply is
p = Qs

8. 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

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

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

11. 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

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

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

14. 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.

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

16. 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.

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

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

19. 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

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

21. 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.

22. 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

23. 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.

24. 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”

25. 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

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

27. 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 =

28. 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