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- Consider the production function Q = 2(KL)0.5 What is the marginal product of labour and capital What is the marginal rate of technical substitution of labor for capital What is the elasticity of substitution at a point K = 1, L = 1 if we increase K by one unit?Given the production function: Where CES stands for Constant Elasticity of Substitution. K is capital and L is labor. The price per unit produced is p, interest (unit price K) is r and wages (unit price L) are w. Find the profit function π(K,L) and simplify Find the first order conditions to maximize the profitConsider the following production functions F(L,K)=LK^3 F(L,K)=L+3K (a) Discuss if each marginal product is diminishing, constant or increasing (b) Calculate the marginal rate of technical substitution (c) Calculate if the function exhibits constant,increasing, or diminishing returns to scale
- Given the production function: Where CES stands for Constant Elasticity of Substitution. K is capital and L is labor. The price per unit produced is p, interest (unit price K) is r and wages (unit price L) are w. a) Find the profit function π(K,L) and simplify b) Find the first order conditions to maximize the profit c) Find the value function for L and K, i.e the functions L* = L*(p,r,w) and K* = K*(p,r,w) and simplify. What is the meaning of the value functions d) Find the best production quantity and the maximum profit, i.e Q*(P,r,w) and π*(P,r,w) simplify resultsConsider the following production function: Q = 2K + 8L. Capital (K) is on the vertical axis and Labour (L) is on the horizontal axis. Q refers to output. Calculate the absolute value of the Marginal Rate of Technical Substitution for this isoquant.A firm is currently producing 500 units of output daily by employing 60 units of labor daily at a price of $10 per unit and 30 units of capital daily at a price of $20 per unit. The marginal product of the last unit of labor employed is 3, and the last unit of capital employed is 5. a. Given the above information, what does the firm's marginal rate of technical substitution, MRTSL,K, equal? b. Indicate on the following diagram some point labeled A that is consistent with the information given in the question.
- A firm has a production function of Q = KL + L, where MPL = K + 1 and MPK = L. The wage rate (W) is $100 per worker and the rental (R) is $100 per unit of capital. The firm is producing 100 units of output. In the long run, what is the firm's Marginal Rate of Technical Substitution?Consider the following production function: f (A, B) = gamma multiply A^alpha multiply B^Beta. where A and B are the inputs and alpha, Beta, gamma are in the set (0,1). Let wA and wB the price of the two inputs. Assume wA, wB > 0. Is the production function separable?Does the production function exhibit constant returns of scale?Compute the cost function and the conditional input demand function.How do these three functions react to a change in wA? Suppose the price of both inputs double, what happens to the conditional input demand function? And to the cost function? Suppose the desired level of output double, what happens to the conditional input demand function? And to the cost function?…Given the production function y= f(x1,x2)=x11/3x21/3. The amount of x2 is equal to 216 in the short run. Calculate the factor demand function Given the product price (P) is 6 and the price of factor 1 (w1) is 12, calculate the optimum amount of factor 1. Show your results on a graph.
- Consider the long-run cost minimisation problem, with L on the horizontal axis and K on the vertical axis as usual. If the marginal rate of technical substitution for a cost minimizing firm is -8, and the rental rate of capital $5, what is the wage rate for labor? Group of answer choices 0.625 40 0.025 1.6Your company operates with a technology that is characterized by a diminishing rate of technical substitution of labor for capital. Your firm is currently producing 64 units of output using 8 units of capital and 10 units of labor. At that operating point the marginal product of labor is 8 and the marginal product of capital is 4. The rental price of a unit capital is $4 and the wage rate is $2 Is your firm minimizing the total long-run cost of producing the 64 units of output? If so, how do you know? If not, show why not and indicate whether the firm should be using more capital and less labor, or less capital and more labor to produce an output of 64.With a production function like Y=zN, which of the following must be true at the optimum? A).The marginal product of labor is smaller than real wage. B).The marginal product of labor is bigger than real wage. C).The representative firm makes positive profits. D). Profits of the representative firm are zero.