Chapter 11, Problem 1CACQ

(A)

To determine

Optimal per unit price in case of monopolist is to be calculated.

Explanation of Solution

E = E_F = E_M

E = -2

MC = $150

ATC = $225

Under monopoly firm,

  $P=\frac{E}{1+E}\times MC$

  $P=\frac{-2}{1+(-2)}\times 150$

  $P=\frac{-2}{-1}\times 150$

  $P=\$300$

Price under monopolist is $300.

(B)

To determine

Optimal per unit price when firm compete against one firm in Cournot oligopoly is to be ascertained.

Explanation of Solution

Competing against one other firm in Cournot Oligopoly, N = 2

  $P=\frac{E}{1+E}\times MC$

  $P=\frac{NEM}{1+NEM}\times MC$

  $P=\frac{2(-2)}{1+2(-2)}\times 150$

  $P=\frac{-4}{-3}\times 150$

  $P=\$200$

Therefore, price is $200.

(C)

To determine

Optimal per unit price when firm compete with 19 other firms is to be ascertained.

Explanation of Solution

Competing against other 19 firms in Cournot Oligopoly , N = 20

  $P=\frac{E}{1+E}\times MC$

  $P=\frac{NEM}{1+NEM}\times MC$

  $P=\frac{20(-2)}{1+20(-2)}\times 150$

  $P=\frac{-40}{-39}\times 150$

  $P=\$153.84$ .

Therefore , Price is $153.84