Question

The demand for slurpees in a competitive market is P=100-2Q and supply is P=Q. What is the equilibrium price and quantity? What is the value of the area of consumer surplus? What is the value of the area of producer surplus? What are the gains to trade in the market? Suppose the slurpee market is monopolized by one firm. Assume the supply function now represents the monopolist’s marginal costs schedule. The demand schedule is unchanged. What is the monopolist’s marginal revenue mathematically? With a monopoly, what is the equilibrium price and quantity? What is the value of the area of consumer surplus? What is the value of the area of producer surplus? What are the gains to trade in the market? What is the value of the area of deadweight loss?

Answer 1

The demand for Slurpee in a competitive market is P=100-2Q and supply is P=Q.

1) What is the equilibrium price and quantity?

100 – 2Q = Q

Q = 100/3 and P = 100/3

2) What is the value of the area of consumer surplus?

CS = 0.5*(100 – 100/3)(100/3) = 1111.11

3) What is the value of the area of producer surplus?

PS = 0.5*(100/3)*(100/3) = 555.55

4) What are the gains to trade in the market?

Gains to the market = Total surplus = PS + CS = 1111.11 + 555.55 = 1666.66

Suppose the Slurpee market is monopolized by one firm. Assume the supply function now represents the monopolist’s marginal costs schedule. The demand schedule is unchanged.

5) What is the monopolist’s marginal revenue mathematically?

MR = d(TR)/dQ = d(100Q – 2Q^2)/dQ = 100 – 4Q

6) With a monopoly, what is the equilibrium price and quantity?

MC = P = Q. MR = MC, which gives 100 – 4Q = Q

100 = 5Q

Q = 20, P = 100 -2*20 = 60

7) What is the value of the area of consumer surplus?

CS = 0.5*(100 – 60)*20 = 400.

8) What is the value of the area of producer surplus?

PS = 0.5*(60 + 40)*20 = 1000

9) What are the gains to trade in the market?

PS + CS = 400 + 1000 = 1400

10) What is the value of the area of deadweight loss?

DWL = 0.5*(60 – 20)*(100/3 – 20) = 266.67