Question

I need help with how to solve the problem so please show work so I can learn.

Suppose a Cobb-Douglas Production function is given by the following: P(L,K) = 20LC- 90.1 where L is units of labor, K is units of capital, and P(L, K) is total units that can be produced with this labor/capital combination. Suppose each unit of labor costs $500 and each unit of capital costs $1,000. Further suppose a total of $200,000 is available to be invested in labor and capital (combined). A) How many units of labor and capital should be "purchased to maximize production subject to your budgetary constraint? Units of labor, L = Units of capital, K = B) What is the maximum number of units of production under the given budgetary conditions? (Round your answer to the nearest whole unit.) Max production units

Answer 1

PCL,K) = 20449 Kol each unit of labour cost is $500 cach unit of capita cost is $2000 Total availash amount "s$ 200,000 500L + foot = 200,000 let G(L,*) = 500L + 1000k - 200,000 = 0 Form Legrange multiphens I(L,k) = P(Lk) + (L,K) L(L) + x(500L +1000k - 209000) 202.9kol dd OL 50 =) 20.00.9160.9-!**!+ (500) = 0 -18_-6.0.1 IL ak = 20coa (0.1k 500 0.1-1 ++ (1000) = 0 -2L09-0-9 1000 A =) -18L01 -260.9 k-49 500 100 K (18) 500L t loook = 200,000 524 (8K) + 1000 K = 200 000 =) K = 20 L-K(18) = 20/18 = 360 Pmax = P(360,20) = 20 (360104(20) 69 5392.6873 53 13 360 20 P = 5343