Consider the following CES production function: Q= AlaL +1-a)K-]%, capital, respectively where Q is output and L and...
a firm produces output according to the production function Q=4K+8L where K is capital and L is labour. in this production function are capital and labour (a) perfect complements (b) perfect substitutes (c) imperfect substitutes or (d) perfect substitues as long as labour is less than 8 and perfect complements when labour is more than 8.
6. a) Consider the following Cobb-Douglas production function: Q AK°L where Q output, K labour, L labour Express the above function in a logarithmic form
Consider the following production function Q(K,L)=100(?^1/2 + ?^1/2 )^2/3 where K is capital and L is labor. 1.1) Determine the returns of scale. 1.2) Find the output elasticity for the production function. 1.3) Interpret your answer in part (1.2)?
Consider the production function given by y = f(L,K) = L^(1/2) K^(1/3) , where y is the output, L is the labour input, and K is the capital input. (a) Does this exhibit constant, increasing, or decreasing returns to scale? (b) Suppose that the firm employs 9 units of capital, and in the short-run, it cannot change this amount. Then what is the short-run production function? (c) Determine whether the short-run production function exhibits diminishing marginal product of labour. (d)...
Consider a firm whose production is given by Q(K, L) = K^1/2 L^1/2, where K and L are the quantities of capital and labour production inputs. Prices of capital and labour are both $2 per unit. (a) Suppose that, in the short run, capital is fixed at 4 units. What would be the minimum cost of producing 20 units of output? Illustrate your answer. (b) Now suppose that, in the long run, both capital and labour are variable. What would...
1. Consider a firm that has the following CES production function: Q = f(L,K) = [aLP + bK°]!/p where p a. Derive the MRTS for this production function. Does this production function exhibit a diminishing MRTS? Justify using derivatives and in words. What does this imply about the shape of the corresponding isoquants? (10 points) b. What are the returns to scale for this production function? Show and explain. Explain what will happen to cost if the firm doubles its...
A firm has the following production function, where Q is output, K is capital and L is labor: Q = 400K0.5L0.3 Does this firm operate under increasing, decreasing or constant returns to scale, and why?
Specific Output Functions, Q = f(L,K): Below are some specific output functions. For each production function (1) Explain how the firm uses the inputs capital (K), and labor (L): (2) Provide an illustration of the corresponding isoquants the preference yield - include three isoquants with unique levels of output; (3) Provide a general form of the production function and create two specific production functions; and (4) Calculate the MRTS Lx for each of your proposed production functions (if possible). (1)...
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)
Consider a firm that has the following CES production function: Q = f(L,K) = [aL^ρ + bK^ρ]^1/ρ where ρ ≤ 1. Please clearly show each STEP and make sure your handwriting is LEGABLE. Thank you Derive the MRTS for this production function. Does this production function exhibit a diminishing MRTS? Justify using derivatives and in words. What does this imply about the shape of the corresponding isoquants? (10 points) What are the returns to scale for this production function? Show...