Show that if the production function is homogeneous of degree 2, then the cost minimizing demand...
Show that if the production function is homogeneous of degree 2, then the cost minimizing demand for input i is given by: xi = h(w) √y, where y and w are output and input prices and h(w) is some function of input prices.
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Show that if the production function is homogeneous of degree 2,
then the cost minimizing demand...
Consider a cost-minimizing firm that uses two inputs x, and x, to produce output y from...
Consider a cost-minimizing firm that uses two inputs x, and x, to produce output y from the production function y=x"X, where a >0 and B>0. The competitive input prices of x, and x, are given respectively as w, and wz. a) Find the firm's demand functions for inputs x, and xz. b) Find the firm's total cost, average cost, and marginal cost functions. c) Show that if a +B>1 then average cost is always greater than marginal cost.
5. Prove that when the production function is homogeneous of degree one, it may be as...
5. Prove that when the production function is homogeneous of degree one, it may be as f(x) 2MP(x)x where MPi(x) is the marginal product of input i. Hint use Euler's Theorem. 6. Derive the cost function for the linear technology y f(xix2)-axi+bx 7. Given the production function fxi)aIxa In(x), derive the firm's supply function assuming an interior solution, assuming that a>0 and a 0. 8. Consider a duopoly facing an industry demand function, p-a-bQ, where Q tg respective cost functions...
Question 4 Consider the production process with 2 inputs and 1 output. The production function is...
Question 4 Consider the production process with 2 inputs and 1 output. The production function is given by y The input prices are w and w2 respectively. Consider the case of long run where both factors are variable. The output price is denoted as p. (Please leave the numbers in decimals or fractions.) 1/3 1/3 (a) First, consider the profit maximization problem directly. Derive the input demand functions and output function in terms of input prices w, and output price...
A cost minimizing firm’s production function is Q=2KL. The price of labor, w, is currently $4,...
A cost minimizing firm’s production function is Q=2KL. The price of labor, w, is currently $4, and the price of capital, r, is currently $1. At the firm’s current level of output, it has total costs of $160. Input prices change such that the wage rate is now 8 times the rental rate. The firm adjusts its input combination, but leaves total output unchanged. Answer the questions below as you solve for the cost - minimizing input combination after the...
2. Marginal products, RTS, and elasticity of substitution: Consider the following production function: q=k *11/4 a....
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...
3. A firm has the production function y 5Z1 + Z2- Input prices are w,-9 and...
3. A firm has the production function y 5Z1 + Z2- Input prices are w,-9 and W2 = 3 a) What is the cost minimizing input bundle? b) What is the minimum cost to produce 100 units of output?
please show all work, thanks! Problems 1 a) A firm has the production function y =...
please show all work, thanks!
Problems 1 a) A firm has the production function y = 22212 and faces input prices W1 and w2. Derive the conditional input demand functions for both inputs. b) If W, = $5 and W2 = $10, what is the minimum cost of producing 27 units of output?
Is the following production function homogeneous? If so, find the degree of homogeneity and comment on...
Is the following production function homogeneous? If so, find the degree of homogeneity and comment on the returns to scale! Q = 4K L This production function homogeneous What is the degree of homogeneity of the production function? This function displays returns to scale.
Is the following production function homogeneous? If so, find the degree of homogeneity and comment on...
Is the following production function homogeneous? If so, find the degree of homogeneity and comment on the returns to scale. Q=3K*24 +Kº24 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. and the function exhibits increasing returns to scale. O A. This function is homogeneous. The degree of homogeneity is (Type a whole number.) and the function constant returns to scale. OB. This function is homogeneous. The degree of homogeneity is (Type...
1. A firm uses labor and machines to produce output according to the production function f(L,...
1. A firm uses labor and machines to produce output according to the production function f(L, M) 2L2 M , where L is the number of units of labor used and M is the number of machines. The cost of labor is $20 per unit and the cost of using a machine is $5. a. Suppose that the firm wants to produce its output in the cheapest possible way. Find the input demand functions for machines and workers. Please show...
Consider a cost-minimizing firm that uses two inputs x, and x, to produce output y from the production function y=x"X, where a >0 and B>0. The competitive input prices of x, and x, are given respectively as w, and wz. a) Find the firm's demand functions for inputs x, and xz. b) Find the firm's total cost, average cost, and marginal cost functions. c) Show that if a +B>1 then average cost is always greater than marginal cost.
5. Prove that when the production function is homogeneous of degree one, it may be as f(x) 2MP(x)x where MPi(x) is the marginal product of input i. Hint use Euler's Theorem. 6. Derive the cost function for the linear technology y f(xix2)-axi+bx 7. Given the production function fxi)aIxa In(x), derive the firm's supply function assuming an interior solution, assuming that a>0 and a 0. 8. Consider a duopoly facing an industry demand function, p-a-bQ, where Q tg respective cost functions...
Question 4 Consider the production process with 2 inputs and 1 output. The production function is given by y The input prices are w and w2 respectively. Consider the case of long run where both factors are variable. The output price is denoted as p. (Please leave the numbers in decimals or fractions.) 1/3 1/3 (a) First, consider the profit maximization problem directly. Derive the input demand functions and output function in terms of input prices w, and output price...
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...
3. A firm has the production function y 5Z1 + Z2- Input prices are w,-9 and W2 = 3 a) What is the cost minimizing input bundle? b) What is the minimum cost to produce 100 units of output?
please show all work, thanks!
Problems 1 a) A firm has the production function y = 22212 and faces input prices W1 and w2. Derive the conditional input demand functions for both inputs. b) If W, = $5 and W2 = $10, what is the minimum cost of producing 27 units of output?
Is the following production function homogeneous? If so, find the degree of homogeneity and comment on the returns to scale! Q = 4K L This production function homogeneous What is the degree of homogeneity of the production function? This function displays returns to scale.
Is the following production function homogeneous? If so, find the degree of homogeneity and comment on the returns to scale. Q=3K*24 +Kº24 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. and the function exhibits increasing returns to scale. O A. This function is homogeneous. The degree of homogeneity is (Type a whole number.) and the function constant returns to scale. OB. This function is homogeneous. The degree of homogeneity is (Type...
1. A firm uses labor and machines to produce output according to the production function f(L, M) 2L2 M , where L is the number of units of labor used and M is the number of machines. The cost of labor is $20 per unit and the cost of using a machine is $5. a. Suppose that the firm wants to produce its output in the cheapest possible way. Find the input demand functions for machines and workers. Please show...
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