Suppose the demand function for a profit maximizing monopolists good is P = 160

Question

Suppose the demand function for a profit maximizing monopolists good is P = 160 - 0.5Q, its total cost function is TC = 20 + 10Q + 0.3Q2, and its marginal cost function is MC = 10 + 0.6Q. If the firm uses a uniform pricing strategy, then rounded to the nearest unit of output and to the nearest dollar the firm will:

A. produce 94 units of output, charge a price of $113, and earn a total profit of $7011

B. produce 94 units of output, charge a price of $113, and earn a total profit of $5894

C. produce 110 units of output, charge a price of $98, and earn a total profit of $8237

D. produce 110 units of output, charge a price of $98, and earn a total profit of $6030

Explanation / Answer

P = 160 - 0.5Q,

TR = P*Q = (160 - 0.5Q)*Q

MR = dTR/dQ = 160 - 2*0.5Q

TC = 20 + 10Q + 0.3Q2

MC = 10 + 0.6Q

For profit to be maximized

MR = MC

160 - Q = 10 + 0.6Q

150 = 1.6Q

Q = 150/1.6 = 94

So P = 160 - 0.5*94 = 113

Total Profit = TR - TC = P*Q - TC

= 94*113 - 20 - 10*94 - 0.3*(94)^2

= 10,622 - 20 - 940 - 2,650

= 7011

So its A. produce 94 units of output, charge a price of $113, and earn a total profit of $7011

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