Assume that all firms in a competitive industry have cost curves given by TC = 128 +8q +2q2. Further, the market demand curve is given by: p = 72 - 2Q. In the long-run market equilibrium, profit for each firm equals:Group of answer choices032641024More information is required to answer this question.
Question
Assume that all firms in a competitive industry have cost curves given by TC = 128 +8q +2q2. Further, the market demand curve is given by: p = 72 - 2Q. In the long-run market equilibrium, profit for each firm equals:Group of answer choices032641024More information is required to answer this question.
Solution
To find the long-run market equilibrium profit for each firm, we first need to find the marginal cost (MC), which is the derivative of the total cost (TC) function.
The TC function is given by TC = 128 + 8q + 2q^2.
Taking the derivative of this function with respect to q, we get MC = d(TC)/dq = 8 + 4q.
In a perfectly competitive market, firms set their output (q) such that the price (p) equals the marginal cost (MC).
The market demand curve is given by p = 72 - 2Q.
Since Q = qn (where n is the number of firms), we can rewrite the demand curve in terms of q as p = 72 - 2qn.
Setting MC equal to p, we get 8 + 4q = 72 - 2q*n.
Solving for q, we get q = (72 - 8) / (4 + 2n) = 64 / (4 + 2n).
Substituting q back into the TC function, we get TC = 128 + 8*(64 / (4 + 2n)) + 2*(64 / (4 + 2n))^2.
Subtracting TC from total revenue (TR = pq = (72 - 2qn) * (64 / (4 + 2n))), we get profit = TR - TC.
Without knowing the number of firms (n), we cannot calculate the exact profit. Therefore, more information is required to answer this question.
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