(a) Suppose we have the following production function: Q= Suppose K is fixed in the short- run at 16. State the firm's short-run cost minimization problem given the fixed input. Discuss.< (b) Letr = $200 and w = $300. Derive the short-run cost function so that we have costs as a function of Q: eg C(Q) = ? Show your work/reasoning.< (c) Show that average costs first fall then rise with greater output. Note: look at Q in the range 0 to 100. You can do this in a table or mathematically. Why does AC fall then rise? < (d) State the firm's profit maximizing problem. (e) Let P = $600. Find optimal output where r = $200 and w = $300. You can do this in a table or mathematically. What are profits? < (f) A break-even price is one where the best a firm can do is earn zero profits. That is, total revenues equal total costs. How is the break-even price related to average costs? Explain. < fac
(a) Suppose we have the following production function: Q= Suppose K is fixed in the short- run at 16. State the firm's short-run cost minimization problem given the fixed input. Discuss.< (b) Letr = $200 and w = $300. Derive the short-run cost function so that we have costs as a function of Q: eg C(Q) = ? Show your work/reasoning.< (c) Show that average costs first fall then rise with greater output. Note: look at Q in the range 0 to 100. You can do this in a table or mathematically. Why does AC fall then rise? < (d) State the firm's profit maximizing problem. (e) Let P = $600. Find optimal output where r = $200 and w = $300. You can do this in a table or mathematically. What are profits? < (f) A break-even price is one where the best a firm can do is earn zero profits. That is, total revenues equal total costs. How is the break-even price related to average costs? Explain. < fac
Chapter10: Cost Functions
Section: Chapter Questions
Problem 10.4P
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Transcribed Image Text:(a) Suppose we have the following production function: Q=K¹/4L³/4 Suppose K is fixed in the short-
run at 16. State the firm's short-run cost minimization problem given the fixed input. Discuss.<
(b) Let r = $200 and w = $300. Derive the short-run cost function so that we have costs as a
function of Q: eg C(Q) = ? Show your work/reasoning.<
(c) Show that average costs first fall then rise with greater output. Note: look at Q in the range 0 to
100. You can do this in a table or mathematically. Why does AC fall then rise? <
(d) State the firm's profit maximizing problem.<
(e) Let P = $600. Find optimal output where r = $200 and w = $300. You can do this in a table or
mathematically. What are profits? <
(f) A break-even price is one where the best a firm can do is earn zero profits. That is, total
revenues equal total costs. How is the break-even price related to average costs? Explain. <
(g) What is the break-even price if r = $200 and w = $300? Explain/show. <
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