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9) A firm's production function is q = 26x0.33 70.67. If the firm is minimizing costs...
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...
Suppose the firm's production function is Q = K1/3L2/3. a. If the rental rate of capital...
Suppose the firm's production function is Q = K1/3L2/3. a. If the rental rate of capital R = $30 and the wage rate W = $40, what is the cost-minimizing capital-to-labor ratio? b. If the rental rate of capital R is $35 and the wage rate W is $70, and assuming the same production function, how many units of labor and capital should the firm use to produce 12 units of output? c. What is the total cost of producing...
Consider a firm which produces a good, y, using two factors of production, xi and x2. The firm's production functio...
Consider a firm which produces a good, y, using two factors of production, xi and x2. The firm's production function is 1/2 1/4 = xi X2. (4) Note that (4) is a special case of the production function in Question 1, in which 1/4 1/2 and B a = Consequently, any properties that the production function in Q1 has been shown to possess, must also be possessed by the production function defined in (4). The firm faces exogenously given factor...
9. Suppose the firm's production function is given by f(K,L) = min (Kº,L"} (a) For what values of a will the firm e...
9. Suppose the firm's production function is given by f(K,L) = min (Kº,L"} (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at K = 10,000 and a = 1. Assuming that the firm wants to produce less than 100 units, derive 10. Consider the production function: f(K,L)=KLI. Let w...
For Question 1-4, use the following information: A firm's production function is gives as: q=3K0.6 L0.4 and its cost...
For Question 1-4, use the following information: A firm's production function is gives as: q=3K0.6 L0.4 and its cost minimizing choice of inputs is L=250 and K=400 1. What is the value of MRTS at the firm's cost minimizing choice of input? 2. If the wage that the firm's pay to hire one unit of labor is 10, what is the user cost of capital? (Graph questions) <--- (Really important - please give clear steps and explanation) 3. Write down...
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...
A firm's production function is given by Q = 30KL. Unit capital and labour costs are...
A firm's production function is given by Q = 30KL. Unit capital and labour costs are €4 and €4, respectively. Find the values of K and L which minimize total input costs if the production quota is 4320. Use the method of Lagrange or substitution to solve this problem. <=and L = | (Simplify your answers.)
5. A firm produces widgets with production function: q-2vKL. In the short run, the firm's amount...
5. A firm produces widgets with production function: q-2vKL. In the short run, the firm's amount of capital is fixed at K = 100. The rental rate is v = 1 and the wage for L is w= 4. (a) Find the firm's short-run total cost curve (SRTC), short-run average cost curve (SRAC), and the short-run marginal cost (SMC) function. (b) Graph the firm's SAC and SMC using the following levels of production: q 25 and q= 100. (c) Find...
A competitive, cost-minimizing firm has the production function f (x, y) = x + 2y and...
A competitive, cost-minimizing firm has the production function f (x, y) = x + 2y and uses positive amounts of both inputs. If the price of x doubles and the price of y triples, then the cost of production will more than double. The answer is false. It will be exactly doubled. I wanna know how to solve this problem by using isoquant line and isocost line. Please do not copy other's answer.
Suppose a firm has the following production function: Q = 2K L. The marginal product of...
Suppose a firm has the following production function: Q = 2K L. The marginal product of capital is 2L, and the marginal product of labor is 2K. Assume that capital rents for $100 per unit per day, that labor can be hired for $200 per unit per day, and that the firm is minimizing costs. a. The firm will hire units of labor and - units of capital. b. What is the total cost of producing 60 units of output?...
Consider a firm which produces a good, y, using two factors of production, xi and x2. The firm's production function is 1/2 1/4 = xi X2. (4) Note that (4) is a special case of the production function in Question 1, in which 1/4 1/2 and B a = Consequently, any properties that the production function in Q1 has been shown to possess, must also be possessed by the production function defined in (4). The firm faces exogenously given factor...
9. Suppose the firm's production function is given by f(K,L) = min (Kº,L"} (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at K = 10,000 and a = 1. Assuming that the firm wants to produce less than 100 units, derive 10. Consider the production function: f(K,L)=KLI. Let w...
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...
A firm's production function is given by Q = 30KL. Unit capital and labour costs are €4 and €4, respectively. Find the values of K and L which minimize total input costs if the production quota is 4320. Use the method of Lagrange or substitution to solve this problem. <=and L = | (Simplify your answers.)
5. A firm produces widgets with production function: q-2vKL. In the short run, the firm's amount of capital is fixed at K = 100. The rental rate is v = 1 and the wage for L is w= 4. (a) Find the firm's short-run total cost curve (SRTC), short-run average cost curve (SRAC), and the short-run marginal cost (SMC) function. (b) Graph the firm's SAC and SMC using the following levels of production: q 25 and q= 100. (c) Find...
Suppose a firm has the following production function: Q = 2K L. The marginal product of capital is 2L, and the marginal product of labor is 2K. Assume that capital rents for $100 per unit per day, that labor can be hired for $200 per unit per day, and that the firm is minimizing costs. a. The firm will hire units of labor and - units of capital. b. What is the total cost of producing 60 units of output?...
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