For a monopolists product, the demand function is p = 75 - 0.05q, and the cost f

Question

For a monopolists product, the demand function is p = 75 - 0.05q, and the cost function is c = 300 + 35q, where q is number of units, and both p and c are expressed in dollars per unit. At what level of output will profit be maximized? At what price does this occur, and what is the profit? The profit will be maximized at an output of 400 units. (Simplify your answer. Type an integer or a decimal.) The profit will be maximized at a price of exist 55 per unit. (Simplify your answer. Type an integer or a decimal.) When maximized, the profit is exist (Simplify your answer. Type an integer or a decimal.)

Explanation / Answer

Here the demand function is p = 75 - 0.05q and

cost function is c = 300 + 35q

Total profit = Total revenue - Total cost

TP = pq - TC = (75 - 0.05q)q - (300 + 35q) = 75q - 0.05q2 - 300 - 35q

so for profit maximization we should differentiate it with respect to q and for maxmimum profit

d(TP)/dq = 0

75 - 0.1q - 35 = 0

0.1q = 40

q = 400

so Output when proift is maximum = 400 units

Maximum profit will be at price = 75 - 0.05 * q = 75 - 0.05 * 400 = $55

and maximum profit is TPmax = 75q - 0.05q2 - 300 - 35q where q = 400

TPmax = 75 * 400 - 0.05 * 400 * 400 - 300 - 35 * 400 = $7700

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