Question

Assume that you can impose a policy in a certain market that restricts how the firms will decide their output: simultaneously or sequentially. In this market there are only two identical firms, no threat of a new entry, and the output is homogenous. The market demand is d(p) = 300 - 6(p) and the firm’s marginal cost is MC = 5. You have to support your policy using quantitative results, not only your intuition (you will not get any credit without quantitative results). For the policy that imposes that the firms decide simultaneous, the equilibrium total quantity in the market is 80 units and the price is 36.67. Using the results from the second policy, draw a graph (not necessary to scale, but to respect the results that you get) so you can compare the deadweight loss for the two policies (you don’t need to calculate the value for the deadweight loss, but you can compare them) and draw the conclusion.

IMPORTANT: Please show your work when you answer the question. If you do not show your work, if your work has no theoretical support or if the graph is not clear, you might not get any points even if the answer might be the right one.

Answer 1

a) Profit Maximization for Monopoly

Marginal Revenue(MR) = Marginal Cost(MC)

Marginal Revenue(MR) = Total Revenue(TR)/ Total Quantity of goods(Q)

TR = P*Q

Given, Q = 500-10*P, therefore P = (500-Q)/10

TR = ((500-Q)/10)*Q = (500Q - Q^2)/10 = 50Q - (1/10)Q^2

MR = dTR/dQ = 50 - 1/5Q

MC = 10 (given)

MR=MC

  50 - 1/5Q = 10

50Q - 1/5 = 10 Q

40Q = 1/5

Q* = 1/200 = 0.005

Clubbing the value of Q* in demand equation, we will get equilibrium level of price P*

1/200 = 500-10*P

10P = 500 - 1/200

10P* = 100000/200 - 1/200 = 99,999/200

P* = (99,999/200)*(1/10) = 49.99

b)