Answer to Question #163430 in Microeconomics for James taylor

Question

Suppose market demand is Q = 16/p² and the monopoly’s total cost function is

C(Q) = 6 + Q²/8. Calculate the monopoly’s price, output and profit.

If the market were instead supplied competitively by firms, and each firm has the same cost function as given above, at the competitive equilibrium how many firms will survive in this market?

Hint: for the competitive market, start by assuming n firms are in the market, and then use the free entry and exit condition to determine n.

Answer 1

The monopoly produces output at MR = MC, so:

MC = C'(Q) = 0.25Q.

If $Q = 16/p^2$ , then p = 4/Q^0.5, so

$MR = TR'(Q) = 4Q^{0.5}.$

$0.25Q = 4Q^{0.5} ,$

Q = 256 units,

p = 4/16 = 0.25.

If the market were instead supplied competitively by firms, then p = MC, so:

$0.25Q = 4/Q^{0.5},$

Q = 6.35,

p = 2.5.