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11. (10 points) Suppose the firm's output Q is related to capital input K and labour...
Suppose the firm's production function is Q = 2KL where Q is units of output, K...
Suppose the firm's production function is Q = 2KL where Q is units of output, K is units of capital (which are fixed at 2), and L is units of labor. a. What is the firm’s short-run production function? b. Over the labor input usage range of 0 to 5, that is L ranging from 0 to 5, graph the firm’s Total Product curve. c. Derive and graph the firm’s Average Product curve and the Marginal Product curve. Graph/plot them...
The marginal product of labour (MPL) at a particular labour input level (L) corresponds to the...
The marginal product of labour (MPL) at a particular labour input level (L) corresponds to the __ on the total product of labour (TPL) curve. O area under the curve between 0 and a particular level of L area above the curve between 0 and a particular level of L slope of the ray from the (0,0) origin to the particular level of L slope of a tangent line at the particular level of L The average product of labour...
For each of the following production functions, solve for the marginal products of each input and marginal rate of substitution.
For each of the following production functions, solve for the marginal products of each input and marginal rate of substitution. Then answer the following for each: does this production function exhibit diminishing marginal product of labour? Does this production function exhibit diminishing marginal product of capital? Does this production function exhibit constant, decreasing, or increasing returns to scale? Show all your work.(a) \(Q=L+K\)(b) \(Q=2 L^{2}+K^{2}\)(c) \(Q=L^{1 / 2} K^{1 / 2}\)
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.)
4. Suppose that a firm's production function is q = 10KiL, The Marginal Products of Capital...
4. Suppose that a firm's production function is q = 10KiL, The Marginal Products of Capital and Labour are therefore as follows. The firm can rent capital (K) and hire labour (L) at competitive rates. The cost of a unit of labour is 20 and the cost of a unit of capital is 80. (a) Write down the equation for the isocost curve. 0o iad the cos minimisi q0i (c) What is the minimum total cost (C) associated with producing...
1. Suppose that the production function for lava lamps is given by Q = KL -ľ, where is the number of lamps produced pe...
1. Suppose that the production function for lava lamps is given by Q = KL -ľ, where is the number of lamps produced per year, K is the machine-hours of capital, and L is the man-hours of labor. Suppose K = 600. a. Draw a graph of the production function over the range L = 0 to L = 500, putting L on the horizontal axis and on the vertical axis. Over what range of L does the production function...
SM 3. A firm uses capital K, labour L, and land T to produce units of...
SM 3. A firm uses capital K, labour L, and land T to produce units of a commodity, where Q=K2/3+ 1/2+/3 Suppose that the firm is paid a positive price p for each unit it produces, and that the positive prices it pays per unit of capital, labour, and land are r, w, and q, respectively. (a) Express the firm's profits as a function of (K,L,T). Then, find the values of K, L, and T, as functions of the four...
A firm produces output Q by using capital K and labor L in fixed proportions, i.e....
A firm produces output Q by using capital K and labor L in fixed proportions, i.e. Q = F (K ,L ) = min {K, L/3}. The price of a unit of labor is w = 6, the price of a unit of capital is r = 2 and the price of output is p = 20. a) Draw the isoquant for Q = 8. b) Find the marginal product of labor. Suppose that (in part c and d) the...
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)...
2. For each of the following production functions: Q = 3L2 +6K4 Q= V25KL Q =...
2. For each of the following production functions: Q = 3L2 +6K4 Q= V25KL Q = 5V1 + 101K a. Find the marginal product of each input, i.e. MP, and MPx: b. Determine whether the production function exhibits diminishing marginal returns to each input. c. Find the marginal rate of technical substitution, MRTSLK and discuss how it changes as the firm uses more L and less K, holding output constant. d. Determine whether the production function exhibits constant, increasing or...
The marginal product of labour (MPL) at a particular labour input level (L) corresponds to the __ on the total product of labour (TPL) curve. O area under the curve between 0 and a particular level of L area above the curve between 0 and a particular level of L slope of the ray from the (0,0) origin to the particular level of L slope of a tangent line at the particular level of L The average product of labour...
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.)
4. Suppose that a firm's production function is q = 10KiL, The Marginal Products of Capital and Labour are therefore as follows. The firm can rent capital (K) and hire labour (L) at competitive rates. The cost of a unit of labour is 20 and the cost of a unit of capital is 80. (a) Write down the equation for the isocost curve. 0o iad the cos minimisi q0i (c) What is the minimum total cost (C) associated with producing...
1. Suppose that the production function for lava lamps is given by Q = KL -ľ, where is the number of lamps produced per year, K is the machine-hours of capital, and L is the man-hours of labor. Suppose K = 600. a. Draw a graph of the production function over the range L = 0 to L = 500, putting L on the horizontal axis and on the vertical axis. Over what range of L does the production function...
SM 3. A firm uses capital K, labour L, and land T to produce units of a commodity, where Q=K2/3+ 1/2+/3 Suppose that the firm is paid a positive price p for each unit it produces, and that the positive prices it pays per unit of capital, labour, and land are r, w, and q, respectively. (a) Express the firm's profits as a function of (K,L,T). Then, find the values of K, L, and T, as functions of the four...
2. For each of the following production functions: Q = 3L2 +6K4 Q= V25KL Q = 5V1 + 101K a. Find the marginal product of each input, i.e. MP, and MPx: b. Determine whether the production function exhibits diminishing marginal returns to each input. c. Find the marginal rate of technical substitution, MRTSLK and discuss how it changes as the firm uses more L and less K, holding output constant. d. Determine whether the production function exhibits constant, increasing or...
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