1. Consider a monopolist with no production costs. For each of the de- mand func

Question

1. Consider a monopolist with no production costs. For each of the de- mand functions below find the marginal revenue functions. (a) P 10-Q (b) F-10- (c) P 20-Q (d) P= 20-5Q (e) P = 100-Q 2. For each of the demand functions above in question 1, find the optimal price and quantity chosen by the monopolist. Use the graphical method and the calculus method. Check if your answers match. 3. Now assume that the monopolist has a cost function TC 2Q. Find the optimal price and quantity chosen by the monopolist. It is easier to do this using calculus. But try the graphical method if you feel up to it. The difference is that you need to consider the MC line as the horizontal intercept. Once again, the intersection of MR will be at the half way point on this (new) horizontal axis. Continue to assume that the monopolist has a cost function TC- 20 Suppose the monopolist can perfectly price d Find the optimal per unit price and the fixed fee that the monopolist charges under a two part tariff nate (first degree) 5. For each of the demand functions above in question 1, find the elasticity of demand as a function of Q

Explanation / Answer

(1)

Total revenue (TR) = P x Q

Marginal revenue (MR) = dTR/dQ. Therefore,

(a) P = 10 - Q

TR = 10Q - Q2

MR = 10 - 2Q

(b) P = 10 - (Q/2) = 10 - 0.5Q

TR = 10Q - 0.5Q2

MR = 10 - Q

(c) P = 20 - Q

TR = 20Q - Q2

MR = 20 - 2Q

(d) P = 20 - 5Q

TR = 20Q - 5Q2

MR = 20 - 10Q

(e) P = 100 - Q

TR = 100Q - Q2

MR = 100 - 2Q

NOTE: As per Chegg Answering Policy, first multi-part question has been answered.

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