// I want to know why C is incorrect. In a fully competitive market, the price s

Question

// I want to know why C is incorrect. In a fully competitive market, the price should equal to AVC in order to prevent new comer.

If the cost function for John's shoe repair is:

Upper C left parenthesis q right parenthesis equals 100 plus 10 q minus q squared plus one third q cubedC(q)=100+10qq2+13q3,

and its marginal cost function is:

MC equalsMC=10 minus 2 q plus q squared102q+q2,

which of the following is/are the profit-maximizing condition for John's shoe repair if the market is prefectly competitive?

A.

P = 10 minus 2 q plus q squared102q+q2

B.

MR = 10 minus 2 q plus q squared102q+q2

C.

P = StartFraction 100 Over q EndFraction plus 10 minus q plus one third q squared100q+10q+13q2

D.

Both A and B.

Your answer is correct.

E.

All of the above.

Explanation / Answer

Total cost function is as follows -

TC = 100 + 10q - q2 + 1/3q3

Marginal cost function is as follows -

MC = 10 - 2q + q2

In a perfectly competitive market, a firm maximizes profit when it produce that level of output at which price equals marginal cost.

Since, in case of perfectly competitive firm, price is given, therefore, each additional unit sold brings in revenue that is equal to price.

Due to this, in such market, marginal revenue equals price as well.

So, profit-maximization condition can be written as follows -

Price = Marginal cost

or,

Marginal revenue = Marginal cost

In other words, both the following equations are profit-maximzing equations for the perfectly competitive firm,

P = 10 - 2q + q2

MR = 10 - 2q + q2

Hence, the correct answer is the option (D).

NOTE - In a fully competitive market, there is no restriction on the entry of new firms or entry of new firms is free. Thus, there is no price at which new firms can be prevented from entering the market. So, your assumption is altogether wrong.

Price equals average variable cost is analyzed to decide whether the firm should shut down or keep operating and not for preventing the entry of new firms.

Option C is incorrect because in this P is equated with total cost function which is not the profit-maximizing condition in case of perfectly competitive firm.

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