Let Q be defined as the level of output produced and sold. Assume the firm\'s co

Question

Let Q be defined as the level of output produced and sold. Assume the firm's cost function is given by: TC = 20 + 5Q + Q2. The demand for the firm's output, Q, is a function of price, P, given by the relationship: Q = 25 - P. Define the total profit as the difference between total revenue and total cost, and express in terms of Q the total profit function for the firm. (Note: Total revenue equals price per unit times the number of units sold.) Determine the output level where total profits arc maximized. Calculate the total profits and selling price at the profit-maximizing output level. If fixed costs increase from S20 to S25 in the total cost relationship, determine the effects of such an increase on the profit-maximizing output level and total profits.

Explanation / Answer

a. total profits = total revenue -total cost =25Q-Q^2-20-5Q-Q^2= -2Q^2+20Q-20 b. for maximized profit d(total profit)/dQ=0 -4Q+20=0 Q=5 c. price=25-5=20 profit=-2*25+20*5-20=30 d. if fixed cost is changed there will be change in total profit function but profit maximizing output will be same total profit =-2Q^2+20Q-25 for maximized profit d(total profit)/dQ=0 -4Q+20=0 Q=5

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