Chapter 8. Suppose a farmer is a price taker (i.e. perfectly competitive) for soybean sales with a cost function given by TC=0.1q2 +2q+100 a. Find the marginal cost function. b. What is this firms supply curve? Hint: Supply curve expresses q (quantity) as a function of P (price). c. What is the profit maximizing level of output in the long-run? d. What is the long-run profit for this firm? f. Suppose the farmer has to purchase a license for $50 per period in order to stay in business. In this case, what is its marginal cost function?
Cost function given by TC= 0.1q^2 + 2q + 100
a. Marginal cost function is dTC/dq, derivative of total cost = 0.1*2q + 2. Hence MC = 0.2q + 2
b. Firm's supply curve is p = MC
0.2q + 2 = p
q = 5*(p - 2)
q = 5p - 10.
This is the supply function
c. Profit maximizing level of output in the long-run is determined at P = MC = AC
0.2q + 2 = 0.1q + 2 + 100/q
q^2 = 1000
q = 31.62
d. Long-run profit for this firm is 0 because in the long run price is equal to AC
f. Marginal cost does not change if there is an increase the fixed cost. Hence it is still 0.2q + 2.
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