Question

In: Economics

A firm with market power faces the following estimated demand and average variable cost functions: Qd...

A firm with market power faces the following estimated demand and average variable cost functions:

Qd = 39,000 - 500P + 0.4M - 8,000PR

AVC = 30 - 0.005Q + 0.0000005Q2

where Qd is quantity demanded, P is price, M is income, and PR is the price of a related good. The firm expects income to be $40,000 and PR to be $2. Total fixed cost is $100,000. What price should the firm charge in order to maximize profit?

		$42.50
		$62
		$48
		$50
		$70

Expert Solution

The demand function of the firm would be:

QD=39,000 - 500P + 0.4M - 8,000PR

=39000-500P+0.4(40000)-8000(2)

=39000-500P

And P=39000-Q/500

=78-0.002Q

MR would be 78-0.004Q

MC would be:dTC/dQ = 30-0.01Q+0.0000015Q^2

Setting MC= MR

78-0.004Q=30-0.01Q+0.0000015Q^2

78-30=0.004Q-0.01Q+0.0000015Q^2

Or, Q= 8000

Substitute Q=8000 in the Price equation, we have

P=78-0.002(8000)

P=78-16

P=62

option(B)

Rahul Sunny answered 2 years ago

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