II. Perfectly Competitive Market A competitive firm has estimated its average va
ID: 1200688 • 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
AVC = 20 - 0.04Q + 0.00005Q2
TC = AVC*Q = 20Q - 0.04Q2 + 0.00005Q3
Total fixed cost is $500
a. SMC = dTC/dQ = 20 - 2*0.04Q + 3*0.00005Q2
= 20 - 0.08Q + 0.00015Q2
b. For AVC Minimum
dAVC/dQ = - 0.04 + 2*0.00005Q
Putting dAVC/dQ = 0
0.04 = 0.0001Q
Q = 0.04/0.0001 = 400
AVC = 20 - 0.04*400 + 0.00005(400)^2
= 12
c. P = $23.60
For max profit
P =MC
23.60 = 20 - 0.08Q + 0.00015Q2
0 = 0.00015Q2 - 0.08Q - 3.60
Q = 575.06
Profit = TR -TC = P*Q - AVC*Q = 23.60*575.06 - 12*575.06 = 6,670.696
d For P =10 ,
Profit is maximized where P = MC
10 = 20 - 0.08Q + 0.00015Q2
0 = 0.00015Q2 - 0.08 + 10
Q = 333.33
Profit = TR -TC = P*Q - AVC*Q = 10*333.33 - 12*333.33 = 666.66
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