Consider a firm whose production is given by Q(K, L) = K^1/2 L^1/2, where K and...
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 be the minimum cost of producing 20 units of output? Illustrate your answer. Explain why your answer here is different from your answer in part (a).
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Consider a firm whose production is given by Q(K, L) = K^1/2 L^1/2, where K and...
Consider the production function given by y = f(L,K) = L^(1/2) K^(1/3) , where y is...
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 with production function f(K,L) = K +L. (a) Suppose that capital level is...
Consider a firm with production function f(K,L) = K +L. (a) Suppose that capital level is currently fixed at K = 10. Find the short term production cost function for producing outputs greater than or equal to 10 units when w = 1 and r=1. (b) Suppose wage goes up to w' = 2 while the price of capital remains same at r = 1. Find the new short-run cost function for producing output greater than or equal to 10...
12. Consider a firm with production function f(K,L) = K+L. (a) Suppose that capital level is currently fixed at K =...
12. Consider a firm with production function f(K,L) = K+L. (a) Suppose that capital level is currently fixed at K = 10. Find the short term production cost function for producing outputs greater than or equal to 10 units when w = 1 and r = 1. (b) Suppose wage goes up to w' = 2 while the price of capital remains same at r = 1. Find the new short-run cost function for producing output greater than or equal...
Output for a simple production process is given by Q = 2KL, where K denotes capital,...
Output for a simple production process is given by Q = 2KL, where K denotes capital, and L denotes labour. The price of capital is $25 per unit and capital is fixed at 8 units in the short run. The price of labour is $5 per unit. What is the total cost of producing 80 units of output? Numeric Answer:
A firm has the production function Q= 4LK. The marginal products are given by MPL =...
A firm has the production function Q= 4LK. The marginal products are given by MPL = 4K and MPK= 4L. Suppose that the prices of labour and capital are given by w and r. Solve for the quantities of L and K that minimize the cost of producing Q units of output. Provide an expression for the long run total cost function. What returns to scale are exhibited by this production function? What economies of scale are exhibited? Show the...
1). Suppose that a firm uses inputs labour (L, measured in person hours) and capital (K, measured in machine hours) in...
1). Suppose that a firm uses inputs labour (L, measured in person hours) and capital (K, measured in machine hours) in the production of its output (Q) according to the production function Q min{2L, 3K} (a) Draw the isoquant line associated with 12 units of output. Measure K along the vertical axis and L along the horizontal axis. (b) Suppose that the price of labour is $2/person hour, and the price of capital is $4 / person hour. What is...
2. Suppose that a firm’s production function is Q = 10 L½ K½ and the unit...
2. Suppose that a firm’s production function is Q = 10 L½ K½ and the unit cost of labor is $20, capital is $80, and the product price is $12 per unit. The firm is currently producing 100 units of output and has determined that its cost minimizing quantities of labor and capital usage for this level of output is 20 and 5 respectively. The product price is $12 per unit. a. Determine the current total cost for 100 units,...
11. Consider the production function: f(K,L)=K+L. Let w and r denote the price of labor and...
11. Consider the production function: f(K,L)=K+L. Let w and r 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. (b) Find the profit maximizing output level and the profit function. 12. Consider a firm with production function f(K,L) = K +L. (a) Suppose that capital level is currently fixed at K = 10. Find the short term production cost function for...
A firm produces output (Q) using inputs of labor (L) and capital (K), whose prices are...
A firm produces output (Q) using inputs of labor (L) and capital (K), whose prices are w and r, respectively. Production is subject to increasing marginal cost. Both inputs are normal. Now suppose w rises. Discuss each of the statements below, explaining whether it is correct or incorrect and why: a) "The increase in w will increase the firm's demand for K as well as its demand for L." b) "If the elasticity of capital-labor substitution (σ) is zero for...
1. A firm has a production function y = VKL, where K, L are positive quantities...
1. A firm has a production function y = VKL, where K, L are positive quantities of capital and labor and y is the quantity of output. Given a positive input prices r for K and w for L, a producer attempts to minimize the cost of producing output y. Assume that w is fixed at 1 for the duration of production planning. (a) Find Cr,y), the minimum cost of producing y as a function of r and output level...
Consider a firm with production function f(K,L) = K +L. (a) Suppose that capital level is currently fixed at K = 10. Find the short term production cost function for producing outputs greater than or equal to 10 units when w = 1 and r=1. (b) Suppose wage goes up to w' = 2 while the price of capital remains same at r = 1. Find the new short-run cost function for producing output greater than or equal to 10...
12. Consider a firm with production function f(K,L) = K+L. (a) Suppose that capital level is currently fixed at K = 10. Find the short term production cost function for producing outputs greater than or equal to 10 units when w = 1 and r = 1. (b) Suppose wage goes up to w' = 2 while the price of capital remains same at r = 1. Find the new short-run cost function for producing output greater than or equal...
Output for a simple production process is given by Q = 2KL, where K denotes capital, and L denotes labour. The price of capital is $25 per unit and capital is fixed at 8 units in the short run. The price of labour is $5 per unit. What is the total cost of producing 80 units of output? Numeric Answer:
1). Suppose that a firm uses inputs labour (L, measured in person hours) and capital (K, measured in machine hours) in the production of its output (Q) according to the production function Q min{2L, 3K} (a) Draw the isoquant line associated with 12 units of output. Measure K along the vertical axis and L along the horizontal axis. (b) Suppose that the price of labour is $2/person hour, and the price of capital is $4 / person hour. What is...
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