A craft brewery hires 2 0 0 daily workers ( L ) at a wage ( w ) of $ 3 2 , and has 1 0 0 units of capital ( K ) at a rental rate ( r ) of $ 1 6 . If the brewery is minimizing costs, which of the following production functions would result in this hiring mix?

(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. <

Two points, A and B, are on an isoquant drawn with labor on the horizontal axis and capital on the ver- tical axis. The capital-labor ratio at B is twice that at A, and the elasticity of substitution as we move from A to B is 2. What is the ratio of the MRTSL, K at A versus that at B?

An isoquant curve for producing a 10 lb bag of wheat is given as below. What is the Marginal Rate of Technical Substitution (MRTS) at a point (L, K)=(2,9)? Capital 1, 14 $15 14 13 12 11 DRBT6543210 9 8 7 -4 -3 4 3 2,9 3,5 43 52 6,1.5 1 2 3 4 5 6 7 Labor