It is known that the production function of a company is ? = 2?^0.6 × ?^0.4...
It is known that the production function of a company
is ? = 2?^0.6 × ?^0.4
, where K is capital and L
is labor. It is known that the company has funds to purchase as
much raw material
$ 6000. It is known that wage (w) is 3 and capital price per unit
(v) is 2.
a. Determine the isocost function. Explain the meaning of isocost
in economics!
b. Prove that there is a diminishing marginal product!
c. With the Lagrange method, calculate how many companies use K and
L to obtain
maximum output (q).
d. Calculate the maximum output value!
e. Calculate the RTS value and prove that in the optimum condition
RTS =
?÷?
. Give an economic explanation!
f. Use charts to explain optimum conditions!
g. Using graphics, what happens if v becomes 3?
h. Using graphics, what happens if the funds the company has
become
Homework Answers
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It is known that the production function of a company
is ? = 2?^0.6 × ?^0.4...
4. Davy Metal Company produces brass fitings. Davy's engineers estimate the production function represented below as...
4. Davy Metal Company produces brass fitings. Davy's engineers estimate the production function represented below as relevant for their long-run capital-labor decisions. 500L0.6K0.8, where Q- annual output measured in pounds, L - labor measured in person hours, K -capital measured in machine hours. The marginal products of labor and capital are therefore MPL-300L-0.4K0.8 MPK-400L0.6K-0.2 Davy's employees are relatively highly skilled, so labour costs 15 per hour. The firm estimates a rental charge of є50 per hour on capital. Davy forecasts...
1. There is a furniture manufacturer using labor (L) and capital (K) to produce tables. Its production function is given by q= 10L^.75 K^.40. It pays a wage of $5 per hour and rents capital at a rate...
1. There is a furniture manufacturer using labor (L) and capital
(K) to produce tables. Its production function is given by q=
10L^.75 K^.40. It pays a
wage of $5 per hour and rents capital at a rate of $15. The firm
wants to find the cost-minimizing bundle of inputs to produce
10,000 tables. Assume K is on the y-axis in what
follows.
Write out the firm’s cost function.
Calculate the firm’s isocost equation.
What is the slope of the...
QUESTION 8 (13 points) A rice processing company estimates that it's production function is given by:...
QUESTION 8 (13 points) A rice processing company estimates that it's production function is given by: Q=F(L,K)= 2006 0.4 where L is the number of workers (labor) and K is units of capital. The wage rate of labor is RM40 and per unit while capital cost is RM50 per unit, and the total input budget is RM5,000. If the firm maximizes output subject to the budget constraint, determine: a. the optimum number of units of labor and capital to be...
Using the production function Q = ( and output levels of Q=2, Q=4, Q=6 A). Suppose...
Using the production function Q = (
and output levels of Q=2, Q=4, Q=6
A). Suppose the price of L and K is $3/hr. On a graph show
isocost lines corresponding to total costs of $12, $24, and $36.
Using isoquants and isocost lines, locate three points on the
expansion path and draw the expansion path. Show your
calculations.
B). Using the three points on the expansion path, calculate the
firm's long run total and average costs at each of...
Use the production function graph to answer the questions. Calculate the marginal product of the first...
Use the production function graph to answer the questions. Calculate the marginal product of the first unit of capital first unit: units Y =f(K) Calculate the marginal product of the second unit of capita o 4 second unit: units What happens to the marginal product of each additional unit of capital, all else equal? 0 1 2 3 456 7 8 9 10 Capital (K) Capital decreases output at a diminishing rate. Capital increases output at a diminishing rate. Capital...
1. Sketch the production isoquant for a production function that takes two inputs (e.g. y = f[l,k]). Show the cost minim...
1. Sketch the production isoquant for a production function that takes two inputs (e.g. y = f[l,k]). Show the cost minimizing combination of inputs by adding an isocost line to your sketch. (a) What is the relationship between the trs and the relative price of one input compared to the other at the cost minimizing combination of inputs? (b) What does the assumption of a diminishing technical rate of substitution (trs) mean? (What does a diminishing trs mean imply for...
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...
Priyanka's company has the production function Q=100K^0.5L^0.5, where Q measures output, K measures machine hours, and...
Priyanka's company has the production function Q=100K^0.5L^0.5, where Q measures output, K measures machine hours, and L measures labor hours. Suppose that the rental rate of capital is R=$30, the wage rate is W=$15, and the firm wants to produce 5,000units of output. Use the Lagrange method to find the optimal input mix. What the optimal level of K & L?
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:...
Derive the cost function associated with the production function in questions 2 is C(q) = 4...
Derive the cost function associated with the production function
in questions 2 is C(q) = 4 + 2q and in questions 3 is
C=wL+rK=1*8+2*4=16. The cost function is of the general form C(Q) =
xQ. What is the value of x?
2. The inverse market demand function is given by P()-20 q. Would consumers prefer to face a monopolist in this market with a cost function given by C(g)4+ 2q, or a perfectly competitive firm with a cost function given...
4. Davy Metal Company produces brass fitings. Davy's engineers estimate the production function represented below as relevant for their long-run capital-labor decisions. 500L0.6K0.8, where Q- annual output measured in pounds, L - labor measured in person hours, K -capital measured in machine hours. The marginal products of labor and capital are therefore MPL-300L-0.4K0.8 MPK-400L0.6K-0.2 Davy's employees are relatively highly skilled, so labour costs 15 per hour. The firm estimates a rental charge of є50 per hour on capital. Davy forecasts...
1. There is a furniture manufacturer using labor (L) and capital
(K) to produce tables. Its production function is given by q=
10L^.75 K^.40. It pays a
wage of $5 per hour and rents capital at a rate of $15. The firm
wants to find the cost-minimizing bundle of inputs to produce
10,000 tables. Assume K is on the y-axis in what
follows.
Write out the firm’s cost function.
Calculate the firm’s isocost equation.
What is the slope of the...
QUESTION 8 (13 points) A rice processing company estimates that it's production function is given by: Q=F(L,K)= 2006 0.4 where L is the number of workers (labor) and K is units of capital. The wage rate of labor is RM40 and per unit while capital cost is RM50 per unit, and the total input budget is RM5,000. If the firm maximizes output subject to the budget constraint, determine: a. the optimum number of units of labor and capital to be...
Using the production function Q = (
and output levels of Q=2, Q=4, Q=6
A). Suppose the price of L and K is $3/hr. On a graph show
isocost lines corresponding to total costs of $12, $24, and $36.
Using isoquants and isocost lines, locate three points on the
expansion path and draw the expansion path. Show your
calculations.
B). Using the three points on the expansion path, calculate the
firm's long run total and average costs at each of...
Use the production function graph to answer the questions. Calculate the marginal product of the first unit of capital first unit: units Y =f(K) Calculate the marginal product of the second unit of capita o 4 second unit: units What happens to the marginal product of each additional unit of capital, all else equal? 0 1 2 3 456 7 8 9 10 Capital (K) Capital decreases output at a diminishing rate. Capital increases output at a diminishing rate. Capital...
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...
Derive the cost function associated with the production function
in questions 2 is C(q) = 4 + 2q and in questions 3 is
C=wL+rK=1*8+2*4=16. The cost function is of the general form C(Q) =
xQ. What is the value of x?
2. The inverse market demand function is given by P()-20 q. Would consumers prefer to face a monopolist in this market with a cost function given by C(g)4+ 2q, or a perfectly competitive firm with a cost function given...
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