Question

Suppose that a firm faces the following demand function: Qd(P) = 7225 - 425P Assuming that MC=9 Calculate the profit maximizing quantity (Q*)

Answer #1

Q=7225-425P can be written as P= (7225-Q)/425 which is inverse demand curve.

Multiplying both sides of inverse demand curve by Q will give us
total revenue which is TR or PQ=(7225Q-Q^{2})/425

The profit is maximized at that point where the marginal revenue is equal to the marginal cost of the firm.

MR can be derived by taking derivative of TR with respect to Q

MR=(7225-2Q)/425

Setting MR equals MC will give us (7225-2Q)/425=9

Q= 1700

The profit maximising quantity of the firm is 1,700 units.

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