Suppose that a firm faces a demand function of the form Q= 60-0.5*P and a cost function

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Question:

Suppose that a firm faces a demand function of the form Q= 60-0.5*P and a cost function C(Q)=30+20Q.

a. Draw the demand curve for this firm, with P on the vertical axis.

b. Show that this firm has constant marginal cost, with MC =20.

c. Using the method that equates the slope of the demand curve with the slope of an iso-profit curve, find the profit-maximizing quantity and price for this firm.

d. The marginal revenue function for this firm is MR=120-4Q. Use this to find the profit-maximizing quantity. This will give the same answer as in part (c).

e. Compute the level of profit this firm makes when it maximizes profit.

f. Compute the profit margin as a percentage of the price at the quantity that maximizes profit.