Part B 3. Consider a competitive firm with these cost functions: TC = q° - 49° +
ID: 1128904 • Letter: P
Question
Part B 3. Consider a competitive firm with these cost functions: TC = q° - 49° + 99 AC = (q - 2)2 + 5 MC = 3q? - 8q + 9 a. In the long run, what q will the firm produce? b. In the long run, what p with the firm charge? C. In the long run, what I will the firm make? d. Evaluate the firm's efficiency in the LR. If the firm with those cost functions becomes a monopoly and faces D: P = 100 - Q MR = 100 - 20 e. What Q will the firm produce? f. What P will the firm charge? g. What I will the firm make? h. Evaluate the firm's efficiency.Explanation / Answer
(3)
(a) In long run, Price = AC = MC
AC = TC/q = q2 - 4q + 9
Equating AC and MC,
q2 - 4q + 9 = 3q2 - 8q + 9
2q2 - 4q = 0
q - 2 = 0 (Assuming q is non-zero and dividing both sides by 2q)
q = 2
(b) When q = 2,
Price = AC = (2 x 2) - (4 x 2) + 9 = 4 - 8 + 9
= 5
(c)
Profit = q x (P - ATC)
In long run, since Price equals ATC, profit is zero.
(d)
In long run, productive efficiency occurs when AC is minimized.
AC is minimized when dAC/dq = 0
2q - 4 = 0
2q = 4
q = 2
Since output corresponding to productive efficiency equals the long run equilibrium output level (obtained in part a), productive efficiency is achieved.
In long run, allocative efficiency occurs when P = MC.
When q = 2 (from part a), MC = (3 x 2 x 2) - (8 x 2) + 9 = 12 - 16 + 9 = 5 = Price
Since Price = MC, allocative efficiency is achieved.
NOTE: As per Chegg answering guidelines, first 4 parts are answered.