Question

7. An Italian sausage maker’s production function is Q = 8k.25 L.25 MPK = 2K-.75 L.75, MPI = 6K.25 L-.25

• Determine the firm’s short-run cost equation (assume K is the fixed input).

• Determine the firm’s long-run cost equation

• If the price of K is $4 and the price of L is $24 and K is fixed at 32 units determine the K, L, Q where the short-run cost equals the long-run cost. What is the cost?

Answer 1

Answer: Q = 8 kº 0.25, 0.25 -0.75 0.25 MP = 20 (0.25)&k. L ək -0.75 0.25 2 k L .0.75 -0.25 k MP = 20 8 (0-25) L ƏL 2 ko.25 1-0.75 ① short rum Cost where k is fixed. let lator Cost wages (w) capital Cost - Rent (or) Cost (C)= WL+ MK here kis fired, hence Cost = wet ne variable fixed Cost Cost whare are variable C = WLtrk all inputs a 3 M= $4, W= $24 K= 32 now, Q = 0 ko.25, 0.25 at Equilibrium MPK=en MPL = W 2 ko -0.75 L K-0.75 0.25 - 4 0.25-27 00

2 ko.25 L-0.75 MPL = w 24 Ik0.25 L-0-15 = 12 ③ 3 calculate value of i from Eq L 10. 0.25 2 -0-75 K-0-75 10.25 L = (k 2 -0.75

K=32 0.25 L = 2 K-0.75 x L = (1.189) Sk L = (1 189) 32 L = 6.725) A = = Coste wet rR Short-run Cost 24 (6.725) + 4(32) 161.4 + 128 Cost = 289.4 now, Coxt where short ron Cost is Equal to long sin Cost

rin Cost shorten Cost a long WLt rk WLt9K 244+ 4X32 = 94L+ 4K When Ik=32 short sm and long sin Costs are equal and cost is $289.4.