A firm uses labor L to produce output Q, using a production function Q = 2L....
A firm uses labor L to produce output Q, using a production
function Q = 2L. The cost of
L is $10 per unit. If the firm needs to produce exactly 200 units
of Q, what will this cost?
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A firm uses labor L to produce output Q, using a production
function Q = 2L....
A small firm uses inputs L & K to produce output Q, and the production function...
A small firm uses inputs L & K to produce output Q, and the production function is Q = K + 4L. The firm needs to produce exactly Q* output. The price of K is $2 and the price of L is $1. What is the firm’s total cost function TC(Q*)?
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...
A firm produces output according to the production function: Q = F(K,L) = 2K + 2L....
A firm produces output according to the production function: Q = F(K,L) = 2K + 2L. a. How much output is produced when K = 2 and L = 3? b. If the wage rate is $65 per hour and the rental rate on capital is $35 per hour, what is the cost-minimizing input mix for producing 4 units of output? Capital: Labor:
A firm uses capital and labor to produce output according to the production q = 4VLK...
A firm uses capital and labor to produce output according to the production q = 4VLK (a) Find the marginal product of labor (MPL) and marginal product of capital (MPK). (b) If the wage w=$1/labor-hr. and the rental rate of capital r-$4/machine-hr., what is the least expensive way to produce 16 units of output? (c) What is the minimum cost of producing 16 units? (d) Show that for any level of output, q, the minimum cost of producing q is...
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?...
Question 7 rding to the production function: uses labor and machines to produce output according to...
Question 7 rding to the production function: uses labor and machines to produce output according to the where Lis ALK) = 41/212, ere is the number of units of labor used and K is the amount of capita or is $40 per unit and the cost of employing capital is $10 per unit. mount of capital employed. The cost (0): On the graph below, draw an isocost line for this firm that includes combin capital and labor that cost $400...
A firm uses labour and capital to produce output according to the production function ??(??, ??) = 4??0.5??0.5, where L...
A firm uses labour and capital to produce output according to the production function ??(??, ??) = 4??0.5??0.5, where L is the number of units of labour and K is the units of capital. The cost of labour is $40 a unit and the cost of capital is $10 a unit. a) On a graph, draw an isocost line for this firm, showing combinations of capital and labour that cost $400 and another isocost line showing combinations that cost $200....
A firm's production function is given by Q=2L"2 +31/2 where Q, L and K denote the...
A firm's production function is given by Q=2L"2 +31/2 where Q, L and K denote the number of units of outputs, labor and capital. Labor cost is $2 per unit, capital cost is $1 per unit and output sells at $8 per unit. Show that the profit function is 1=16L"2 + 24K12 - 2L-K and hence find the maximum profit and the values of Land K at which it is achieved. HINT: do not forget to check the second sufficient...
9. A firm uses capital and labor to produce a single output good. The production function...
9. A firm uses capital and labor to produce a single output good. The production function is given by F(K,L)=K^0.5L, where K is the amount of capital and L is the amount of labor employed by the firm. The unit prices of capital and labor are given by, respectively r=$5 and w=$6. Based on this information, characterize the optimal (output maximizing) allocation of inputs given that the firm decided to limit its total cost to $12,000. Illustrate your solution graphically:...
A production function is given as Q = 21L - 0.06L2. If each unit of output...
A production function is given as Q = 21L - 0.06L2. If each unit of output Q contributes $10 in revenue (sells for $10) and each labor unit costs $42 per hour, how many units of labor (L) should be hired to maximize profit? Given your answer to part c, what output (Q) will the firm produce? Assuming no other cost than labor costs, what is the profit at this level of labor and output Suppose that the marginal...
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...
A firm uses capital and labor to produce output according to the production q = 4VLK (a) Find the marginal product of labor (MPL) and marginal product of capital (MPK). (b) If the wage w=$1/labor-hr. and the rental rate of capital r-$4/machine-hr., what is the least expensive way to produce 16 units of output? (c) What is the minimum cost of producing 16 units? (d) Show that for any level of output, q, the minimum cost of producing q is...
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?...
Question 7 rding to the production function: uses labor and machines to produce output according to the where Lis ALK) = 41/212, ere is the number of units of labor used and K is the amount of capita or is $40 per unit and the cost of employing capital is $10 per unit. mount of capital employed. The cost (0): On the graph below, draw an isocost line for this firm that includes combin capital and labor that cost $400...
A firm's production function is given by Q=2L"2 +31/2 where Q, L and K denote the number of units of outputs, labor and capital. Labor cost is $2 per unit, capital cost is $1 per unit and output sells at $8 per unit. Show that the profit function is 1=16L"2 + 24K12 - 2L-K and hence find the maximum profit and the values of Land K at which it is achieved. HINT: do not forget to check the second sufficient...
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