1 . A competitive firm’stotal cost function is given by TC = .25Q 2 + 25 (with M
ID: 1229025 • Letter: 1
Question
1. A competitive firm’stotal cost function is given by
TC = .25Q2 + 25
(with MC = .5Q).
The firm faces a market price of $15. Algebraicallycalculate the profit maximizing output and the level of optimalprofit for the firm.
(ii) Suppose that fixed costs increaseby $50 but the prevailing market price remainsunchanged. Using algebra determine the effects of this changein cost on the profit maximizing output and the optimalprofit. Do you see any change from your answer to (i)above? Explain why or whynot.
(40)
2. Amonopolist’s demand function is given by
P = 80 – 3Q
(with MR = 80 – 6Q).
Its totalcost function is
TC = 20Q + 200
(with MC = 20).
(i) Using algebra determine the profit maximizing output, price andoptimal profit for the firm.
(ii) Suppose that instead ofmaximizing profit, the firm wants to maximize totalrevenue. Using algebra determine the optimal output, price,profit and revenue for the firm.
(40)
Explanation / Answer
1.) (i.) Remember, the profit maximizing level of output canbe found when price is equal to marginal cost (P = MC) (ii.) TC = TVC + TFC So, given the new TFC (total fixed cost), reconstruct your costfunction then find MC by taking the derivative of the new TCfunction. (Hint: MC will be the same) Then, do the same thing you did for part one. 2.) (i.) For a monopolist, the profit maximizing price can befound at MC = MR from this price, find quantity with the demand function. and profit = TC - TR and total revenue, or TR, is equal to P*Q (ii.) This one isn't as tricky as it seems - I think once youget comfortable with the above problems you'll get it.
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