Question

Consider the market for coffee in Claremont.

QD = 105 – 4P

QS = 75 + 2P

1. What is the Marginal Revenue function in this market?
2. If there was only one coffee firm in this market, solve for the monopoly equilibrium price and quantity.
3. Draw a graph showing this market, including Supply, Demand and MR.
4. What is the deadweight loss if this market operates as a monopoly?

Answer 1

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Solution,

A).

Market Revenue

Q = 105 - 4P

4P = 105 - Q

P = 105/4 - Q/4 = 26.25 - 0.25Q

Total Revenue = P*Q = (26.25 - 0.25Q)Q = 26.25Q - 0.25Q²

Marginal Revenue = 26.25 - 0.50Q

B).

Supply Function is the marginal cost function for the firm

Q = 75 + 2P

P = Q/2 - 75/2 = 0.5Q - 37.5

Marginal Cost = 0.5Q - 37.5

Monopoly equilibrium when MR=MC

Marginal Revenue = 26.25 - 0.50Q

Marginal Cost = 0.5Q - 37.5

26.25 - 0.50Q = 0.5Q - 37.5

26.25 + 37.5 = 0.5Q + 0.5Q

Q = 63.75

P = 26.25 - 0.25Q = 26.25 - 0.25(63.75) = 26.25 - 15.9375 = 10.3125.

Equilibrium Price = 10.3125, Equlibrium Quantity = 63.75

C).

D). DeadWeight loss

difference due to perfect competition equilibrium and monopoly equilibrium

Perfect competition equilibrium where demand function equal to marginal cost

Marginal Cost = 0.5Q - 37.5

Demadn(P) = 26.25 - 0.25Q

Equilibrium when P=MC

26.25 - 0.25Q = 0.5Q - 37.5

63.75 = 0.75Q

Q = 63.75/0.75 = 85

P = 26.25 - 0.25Q = 26.25 - 0.25(85) = 26.25 - 21.25 = 5

Monopoly equlibrium, Equilibrium Price = 10.3125, Equlibrium Quantity = 63.75

Perfect competition equilibrium , Equilibrium Price = 5, Equlibrium Quantity = 85

Dead weight loss = 1/2*(10.3125-5)*(85-63.75) = 1/2*(5.3125*21.25) = 56.44

Dead weight loss is 56.44