Question

A monopolist in the radio industry has two radio-making plants. The marginal cost of radio production by Plant A is $4Q (where Q is the number of radios produced) and the marginal cost of radio production by Plant B is always $16. If the demand curve for radios is downward sloping, the monopolist will

a. never produce more than four radios at Plant A.

b. produce radios at Plant A only as a last resort.

c. never produce radios at Plant A.

d. always produce four times as many radios at Plant B as at A.

Answer 1

Answer: a. Never produce more than four radios at Plant A.

A monopolist produces profit-maximizing output at the level, where marginal revenue(MR) equals the marginal cost(MC).

A monopolist who produces same product in different plants, maximizes his/her profit when,

MR = MC₁ = MC₂ =....= MC_N , where 'N' is the number of plants, the monopolist produces the output; 'MC₁' is the marginal cost of production in plant 1, 'MC₂' is the marginal cost of production in plant 2, and so on.

In the given question, the marginal cost of radio production by the monopolist in plant A is '$4Q' ; and the marginal cost of radio production by Plant B is always $16.

The monopolist maximizes his/her profit, when MR = $4Q = $16

i.e., MR = $16 ; and $4Q = $16

Now, if $4Q = $16

then, Q = $16 / $4 = 4

Thus, to maximize the profit, the monopolist will produce 4 units of output in plant A. If it produces more than 4 units, the MC in plant A will be greater than MR, which is $16. Thus the monopolist will incur loss per unit of output.

So, if the demand curve for radios is downward sloping, the monopolist will never produce more than four radios at Plant A.

A monopolist is a price maker, and faces a downward sloping market demand curve of its product.

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