A. To maximize profit, the firm should produce the level of output where marginal cost equals marginal revenue. In a perfectly competitive market, the market price is also equal to the firm's marginal revenue. Therefore, we set MR = MC:
MR = $10
MC = TC' = 10 - 8q + 3q^2
10 - 8q + 3q^2 = 10
3q^2 - 8q = 0
q(3q - 8) = 0
q = 0 or q = 8/3
Since the second order condition is satisfied (TC'' = -8 + 6q > 0), the output level that maximizes profit is q = 8/3.
B. To determine the level of profit at equilibrium, we need to calculate total revenue and total cost at the output level of q = 8/3:
TR = P*q = $10*(8/3) = $26.67
TC = 10q - 4q^2 + q^3 = 10*(8/3) - 4*(8/3)^2 + (8/3)^3 = $21.33
Profit = TR - TC = $5.33
Therefore, the level of profit at equilibrium is $5.33.
C. To stay in the market, the firm's minimum price should be equal to or greater than its average variable cost (AVC) at the output level of q = 8/3. AVC is calculated by taking the derivative of the total variable cost (TVC) with respect to q and dividing by q:
TVC = 10q - 4q^2 + q^3
AVC = TVC'q^-1 = 10 - 8q + 3q^2
AVC at q = 8/3 is:
AVC = 10 - 8(8/3) + 3(8/3)^2 = $5.33
Therefore, the minimum price required by the firm to stay in the market is $5.33.
1. Suppose that the firm operates in a perfectly competitive market. The market price of his product is $10. The firm estimates its cost of production with the following cost function
TC=10q-4q2+q3
A. What level of output should the firm produce to maximize its profit?
B. Determine the level of profit at equilibrium.
C. What minimum price is required by the firm to stay in the market?
3 answers
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
One day at 3:00 a.m., the temperature was
–
13
°
F
in Kodiak, Alaska. At 10:00 a.m., the temperature was 22°F. What was the average change in temperature per hour?
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
One day at 3:00 a.m., the temperature was
–
13
°
F
in Kodiak, Alaska. At 10:00 a.m., the temperature was 22°F. What was the average change in temperature per hour?
To find the average change in temperature per hour, we need to know how much the temperature changed from 3:00 a.m. to 10:00 a.m.
The temperature change is:
22°F - (-13°F) = 35°F
The time elapsed is:
10:00 a.m. - 3:00 a.m. = 7 hours
The average change in temperature per hour is:
35°F ÷ 7 hours = 5°F/hour
Therefore, the average change in temperature per hour is 5°F/hour.
The temperature change is:
22°F - (-13°F) = 35°F
The time elapsed is:
10:00 a.m. - 3:00 a.m. = 7 hours
The average change in temperature per hour is:
35°F ÷ 7 hours = 5°F/hour
Therefore, the average change in temperature per hour is 5°F/hour.
3 answers