(i) A competitive firm%u2019s total cost function is given by TC = .25Q 2 + 25 (

Question

(i)      A competitive firm%u2019s total cost function is given by

                   TC = .25Q2 + 25

                   (with MC = .5Q).

The firm faces a market price of $15. Algebraically calculate the profit maximizing output and the level of optimal profit for the firm.

   (ii)   Suppose that fixed costs increase by $50 but the prevailing market price remains unchanged. Using algebra determine the effects of this change in cost on the profit maximizing output and the optimal profit. Do you see any change from your answer to (i) above? Explain why or why not.

Explanation / Answer

here MC=MR

TR=MR*P

=0.5Q*Q=0.5Q^2

profit=Tr-Tc

.5Q^2-.25Q^2-25

=.25Q^2-25

profit=.25Q^2-25

profit maximisation

givenP=15

.5Q=15

Q=30

hence fins the profit

Profit=225-25=200

when fixed cost are added

it gets added to the total cost

TC= fixed cost+variable cost

so now TC=

.25Q^2+75

P remains the same

so profit decreases by 50

hence new profit=150

yes a chnage os observed as the fixed cost has a direct impact on the total cost

and profit is total revenue-total cost

so as we increase the total cost the profit decreses

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.