Plz No Bad handwriting 4) Assume that a monopolist faces the following demand cu
ID: 1115925 • Letter: P
Question
Plz No Bad handwriting
4) Assume that a monopolist faces the following demand curve: P-250-2Q. Also assume that the total cost function is given as: TC-1/2 Q2 a) What would be the monopolist price and quantity? Calculate the profit for the monopolist and the DWL Calculate the learner index for this monopolist Now assume that the government imposes a specific tax of $1 per unit. What will happen to price and quantity? What will happen to the profit of the monopolist? The government decides to impose a price ceiling on the monopolist to increase total welfare. What should be the optimal price ceiling? b) c) d)Explanation / Answer
a) Find the MR as MR = dTR/dQ.TR = 250Q - 2Q^2. Hence MR = 250 - 4Q. MC = 0.5*2Q = Q
Find profit maximizing price and quantity for the monopolist
MR = MC
250 - 4Q = Q
Q* = 50 and P = 250 - 2*50 = $150
Profit = TR - TC = 50*150 - 0.5*(50^2) = 6250
DWL = 0.5*(monopoly price - marginal cost at current qty)current qty = 0.5*(150 - 50)*50 = 2500
b) Lerner index = (P - MC)/P = (150 - 50)/150 = 2/3 = 0.67
c) New TC = 0.5Q^2 + Q
MC = Q + 1
New profit maximizing quantity and price are
250 - 4Q = Q + 1
249 = 5Q
Q = 49.8
PRICE P rises to = 250 - 2*49.8 = 150.4
Profits = 150.4*49.8 - (0.5*(49.8^2) + 49.8) = 6200.1. Profits have fallen due to tax
d) Optimal price ceiling would be P = MC.This will be welfare maximizing. This would imply
250 - 2Q = Q
Q* = 83.33 and price P = MC = 83.33
This is welfare maximizing