Question

A perfectly competitive firm in the short run has Total Cost and
Marginal Cost functions given by TC(Q)=9+Q+Q^{2} and
MC(Q)=1+2Q, respectively. The firm faces a price of P=$17.
Determine the output that the firm will produce and the profit.
Show the solution graphically.

Answer #1

Profit is maximized when marginal revenue and marginal cost both are equal.

In perfect competition price and marginal revenue both are equal hence

MR = 17

Equating MR and MC

1 + 2Q = 17

2Q = 16

Q = 8

**Hence the profit-maximizing quantity will be 8
units**

Profit = Total Revenue - Total Cost

Total Revenue = Price x Quantity

Total Revenue = 17 x 8

Total Revenue = 136

Total Cost = 9 + Q + Q2

Total Cost = 9 + (8) + (8)2

Total Cost = 81

Profit = Total Revenue - Total Cost

Profit = 136 - 81

**Profit = 55**

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