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Consider the production function Q = 2(KL)0.5 a) What is the marginal product of labour and capital (1 marks) b) What is the marginal rate of technical substitution of labor for capital (2 marks) c) What is the elasticity of substitution at a point K = 1
2. Marginal products, RTS, and elasticity of substitution: Consider the following production function: q=k *11/4 a. For some w, y, use the Lagrangean method to derive demand functions by finding the cost-minimizing combinations of k and I in terms of q, w, and y (so the cost function is the objective function, and the production function is the constraint). (10 points) b. What is the rate of technical substitution (RTS) for this function? (5 points) C. Presume that the firm...
1. The marginal rate of technical substitution at any particular labor-capital bundle is A. the slope of the isoquant. B. the average product of labor relative to the average product of capital. C. the wage relative to the cost of capital. D. the slope of the indifference curve. E. the ratio of labor to capital. 2. The cross-elasticity of labor with respect to capital is A. the change in labor relative to a change in capital. B. the change in...
2. Find the technical rate of substitution (TRSKL) for the production function 9-(K +3L) A. ***
Consider the Leontief production function F(KL) = min {K,L], where capital K and labor L have respective positive input prices r and w. (a) Why is it that the cost-minimizing firm sets K 5. L? (b) What is the cost function? (c) How would your answer to part (b) change, if at all, if rw 0? Explain.
(a) Consider the production function, q = 100K2L1.5 Calculate the marginal product of labor, MPL, and the marginal product of capital,MPK. (c) Suppose that in the short run, the level of capital is fixed at K = 15. Write out the total product of labor curve. What is the marginal product of labor when L = 100? (d) Now consider two input combinations, (K = 5, L = 100) and (K = 20, L = 25). Which of the two...
1). Consider the production function Q= 10*L0.4 * K0.5 a.) Find the marginal product of labor. b.) Find the marginal product of capital. c.) Is there diminishing marginal product of capital? d.) Find MRTS. e.) If w = 10 and r = 20, find the relationship between optimal level of capital and labor to be used.
10. Consider the production function: f(KL)=K L. Let wandr denote the price of labor and capital, and let p denote the price of the output good. (a) Find the cost minimizing input bundle and the cost function as a function of w., and q. (b) Find the profit maximizing output level and the profit as a function of w, r, and p. 11. Consider the production function: f(KL)=K+L. Let w and r denote the price of labor and capital, and...
1. Suppose f(K,L)=[L+K]3, what is the MRTS? 2. Suppose f(K,L)=K(1/2)+L(1/2) Find the marginal rate of technical substitution. 3. f(K,L)=K(1/2)+L(1/2) Find the marginal rate of technical substitution.
Consider a production function Q=Q(K,L)=6K^(1/2)L^(1/3) with K as capital and L as labor input. Let the price per unit of output be P=$0.50, the cost or rental rate per unit of capital be r=$0.10 and let the price (wage rate) of labor be w=$1. a) find the profit max level of K and L and check with second order condition (my answer was L=3.375 and K=1.5) b) Find max profit (I got profit=1.986)
The production process used 2 inputs: Labor (L) and Capital (K). The production function is Q = min{2L,K} , the price of L is $3 and the price of K is $6. What's the minimum cost that the firm has to pay to produce 8 units?___