Question

Givens: 10 * L +40 * K min L>0, K >0 s.t. 50 < K.25 * L-25 • The marginal product of labor: MP, = .25 * 76 • The marginal product of capital: MPK = .25 * * 1.25 K.75 Equation Description: A firm is attempting to minimize total cost subject to sufficiently employing units of labor and units of capital to produce an output level at least as large as a specified output quota. Total cost equals the cost to employing units of labor plus the cost to employing units of capital. A firm's production function is the product of two terms: the first term is units of capital raised to the 25 power; and, the second term is units of labor raised to the 25 power. The marginal product of labor equals the product of three terms: the first term is.25; the second term is units of capital raised to the 25 power; the third term is units of labor raised to the -75 power. The marginal product of capital equals the product of three terms: the first term is 25; the second term is units of labor raised to the 25 power; the third term is units of capital raised to the -75 power. The wage rate is $10 per unit of labor. The rental rate is $40 per unit of capital. The output quota is 50 units. Question: How many units of capital minimize cost? 8,000 units 10,000 units 1,000 units 4,250 units 5,000 units 300 units

Answer 1

B) W =10, = 40, 0-50, Q = 1.252025 at Eqm MRS K= Wlo=1/4 ķ=1 = 4K=L. fecom proda funch 50 = k 25 ( 4 KJ 25 50= k05 (4) 25 2500 = K (4) · 5 Ko = 2500 = 1250, Ang

doo @ w=60, r=20, Q=1000, at Eqm MAS = wly = 3. Q = 6.25 2.75 MRS = MR = 75 K = 36 from eam 84 from peodo funer - 1000 = K* option 2.) don Q. Min cost Who toka = 1000 (60+20) = 80 x 1000 son = $80,000 An 1000 = )25 ()945 optim 6.)