Question

1. A monopolist has costs given by C = Q and faces demand curve P = 12 - Q. a. Provide a labeled diagram that shows the monopolist's MC, AC, P and MR curves. b. Illustrate and calculate the profit maximizing level of output, price and profits. Calculate the elasticity of demand at the monopoly equilibrium price. Confirm that MR =P(1 + 1/n] d. illustrate and calculate the efficiency loss. e. Calculate the per-unit subsidy required to eliminate the efficiency loss and show it in your diagram. f. Does your diagram suggest that this would be a sensible way to eliminate the Efficiency loss? g. Illustrate Two-Part Tariff

Answer 1

(a)

MC = dC/dQ = 2Q

AC = C/Q = Q

P = 12 - Q

TR = PQ = 12Q - Q2

MR = dTR/dQ = 12 - 2Q

Graph:

P, MR.AC, MRMC 12

(b)

Setting MR = MC,

12 - 2Q = 2Q

4Q = 12

Q = 3

P = 12 - 3 = 9

TR = 9 x 3 = 27

TC = 3 x 3 = 9

Profit = TR - TC = 27 - 9 = 36

In above graph, profit is maximized at point E with price P0 and output Q0.

(c)

Q = 12 - P

Elasticity (E) = (dQ/dP) x (P/Q) = - 1 x (9/3) = - 3

MR = 9 x [1 - (1/3)] = 9 x (2/3) = 6

From MR equation, MR = 12 - (2 x 3) = 12 - 6 = 6, hence proved.

(d)

When P = MC,

12 - Q = Q

2Q = 12

Q = 6

P = 6

Efficiency loss = (1/2) x Change in P x Change in Q = (1/2) x (9 - 6) x (6 - 3) = (1/2) x 3 x 3 = 4.5

In above graph, efficiency loss is area EFG.

NOTE: As per HOMEWORKLIB POLICY, only 1st 4 parts are answered.