II. Perfectly Competitive Market A competitive firm has estimated its average va
ID: 1200418 • Letter: I
Question
II. Perfectly Competitive Market
A competitive firm has estimated its average variable cost function as
AVC = 20 - 0.04Q + 0.00005Q2
Total fixed cost is $500
SHOW ALL WORK
a. The marginal cost function associated with this AVC function is
SMC = _______________.
b. AVC reaches its minimum at _________ units of output at which AVC = __________. The
forecasted price is P = $23.60.
c. To maximize its profit the firm should produce ___________ units of output. Profit (loss) is
____________.
Suppose the forecasted price is P = $10.
d. The firm should produce ____________ units of output for a profit (loss) of $____________.
Explanation / Answer
a. AVC = 20 - 0.04Q + 0.00005Q2
SMC = dAVC/dQ = -0.04 + 2*0.00005Q = -0.04 + 0.0001Q
b. AVC reaches its minimum when AVC = SMC = P
So, -0.04 + 0.0001Q = 23.60
0.0001 Q = 23.64
Q = 236400
AVC = 20 - 0.04Q + 0.00005Q2
= 20 - 0.04* 236400 + 0.00005( 236400)^2
= 20 - 9456 + 2794248
AVC= 2784812
c. Q =236400
Profit = TR - TC = P*Q - TFC - TVC = 10*236400 - 500 - 20 + 0.04(236400) - 0.00005(236400)^2
= 2364000 - 500 - 20 + 9456 - 2794248
= 421,321
d. For max profit , firm should produce where P = MC
10 = -0.04 + 0.0001Q
So, Q = 10.04*10000 = 100400
Profit = TR - TC = P*Q - TFC - TVC = 10*100400 - 500 - 20 + 0.04(100400) - 0.00005(100400)^2
= 1004000 - 500 - 20 + 4016 - 504008
= 503488
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