Question

Suppose that leather is sold in a perfectly competitive industry. The industry short-run supply curve (marginal cost curve) is P = MC = 3Q. The demand for leather hides is given by Q = 60 − P.

a. Find the equilibrium market price and quantity.

b. Suppose that the leather tanning releases bad stuff into waterways. The external marginal cost is $5 per unit. Calculate the socially optimal level of output and price for the tanning industry.

c. What are the total social benefit and total social cost at the market equilibrium?

d. What is the market surplus at the market equilibrium?

e. What are the total social benefit and total social cost at the social optimal point?

f. What is the market surplus at the social optimal point?

g. What is the deadweight loss?

Please use the graph to explain your answer.

Answer 1

We have the following information

Marginal Cost (MC) = 3Q where Q is the quantity of leather

Demand: Q = 60 – P or P = 60 – Q

Marginal External Cost (MEC) = 5Q

Marginal Social Cost (MSC) = MC + MEC

MSC = 3Q + 5Q

MSC = 8Q

Part 1: Equilibrium without external cost

We will equate MC with the demand equation

60 – Q = 3Q

4Q = 60

Equilibrium Quantity = 15

P = 60 – Q

Equilibrium Price = 45

Part 2: Socially optimal level of output and price

We will equate the demand equation with the MSC

60 – Q = 8Q

9Q = 60

Socially Optimal Equilibrium Quantity = 6.67

P = 60 – Q

Equilibrium Price = 53.3

Part 3: Total Social Benefit and Total Social Cost at Market Equilibrium

Total Social Benefit (TSB) is represented by triangle (A0D), and Total Social Cost (TSC) is represented by triangle (ABC)

TSC = Area of the triangle (ABC)

TSC = ½ × (Base) × (Height)

MSC = 8Q

MSC = 8 × 15

MSC = 120

Base = 120 – 45

Base = 75

Height = 15 – 6.67

Height = 8.33

TSC = ½ × 75 × 8.33

TSC = 312.375

TSB = Area of the triangle (A0D)

TSB = ½ × (Base) × (Height)

Base = 60

Height = 6.67

TSB = ½ × 60 × 6.67

TSB = 200.1

Part 4: Market Surplus

Market Surplus = TSB – TSC

Market Surplus = 200.1 – 312.375

Market Surplus = – 112.275

Part 5: Total Social Benefit and Total Social Cost at Social Optimal Point

Total Social Cost = 0

Total Social Benefit (TSB) = Area of the triangle (A0D)

TSB = ½ × (Base) × (Height)

Base = 60

Height = 6.67

TSB = ½ × 60 × 6.67

TSB = 200.1

Part 6: Market Surplus

Market Surplus = TSB – TSC

Market Surplus = 200.1 – 0

Market Surplus = 200.1

Part 7: Deadweight Loss

Deadweight Loss (DWL) = Area of the triangle (ABC)

DWL = ½ × (Base) × (Height)

MSC = 8Q

MSC = 8 × 15

MSC = 120

Base = 120 – 45

Base = 75

Height = 15 – 6.67

Height = 8.33

DWL = ½ × 75 × 8.33

DWL = 312.375

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