Question

A firm’s production function is given by Q = 5K1/3 + 10L1/3, where K and L...

  1. A firm’s production function is given by Q = 5K1/3 + 10L1/3, where K and L denote quantities of capital and labor, respectively.
    1. Derive expressions (formulas) for the marginal product of each input.
    2. Does more of each input increase output?
    3. Does each input exhibit diminishing marginal returns? Prove.
    4. Derive an expression for the marginal rate of technical substitution (MRTS) of labor for capital.
    5. Suppose the price of capital, r = 1, and the price of labor, w = 1.   The firm wants to produce 200 units of output. What quantities of capital and labor would minimize the costs of producing 200 units of output? Show all your work.
Business   Economics   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Consider the following Cobb-Douglas production function: y(K,L) = 2K^(0.4)*L^(0.6), where K denotes the amount of capital...
Consider the following Cobb-Douglas production function: y(K,L) = 2K^(0.4)*L^(0.6), where K denotes the amount of capital and L denotes the amount of labour employed in the production process. a) Compute the marginal productivity of capital, the marginal productivity of labour, and the MRTS (marginal rate of technical substitution) between capital and labour. Let input prices be r for capital and w for labour. A representative firm seeks to minimize its cost of producing 100 units of output. b) By applying...
Cobb-Douglas Production Function & Cost of Production A firm’s production function is given as – q...
Cobb-Douglas Production Function & Cost of Production A firm’s production function is given as – q = 2K0.4N0.6 What kind of returns to scale does this production technology exhibit? Justify your answer. Find out the expression for the marginal product of labor. Find out the expression for the marginal product of capital. Find out the expression for MRTS.
Suppose a competitive firm’s production function is Y= 20 L1/2 K1/3. L is Labor , K...
Suppose a competitive firm’s production function is Y= 20 L1/2 K1/3. L is Labor , K is capital and Y is output. a) (4) Find the marginal product of labor and capital. b) (4) What is Marginal Rate of technical Substitution of Labor for Capital? c) (2) Does this production function exhibit increasing, decreasing or constant returns to scale? Show your work.
Suppose a firm’s production function is given by Q = L 1/2 , K 1/2. a)...
Suppose a firm’s production function is given by Q = L 1/2 , K 1/2. a)   Suppose the firm has a fixed cost FC=6, the price of labor is w = 64 and the price of capital is r = 4. Derive the firm’s total cost function, TC(Q). b)   What is the firm’s marginal cost? c)   Graph the firm’s isoquant for Q = 20 units of output. On the same graph, sketch the firm’s isocost line associated with the total...
A firm has the production function: Q = L 1 2 K 1 2 Find the...
A firm has the production function: Q = L 1 2 K 1 2 Find the marginal product of labor (MPL), marginal product of capital (MPK), and marginal rate of technical substitution (MRTS). Note: Finding the MRTS is analogous to finding the MRS from a utility function: MRTS=-MPL/MPK. Be sure to simplify your answer as we did with MRS. A firm has the production function: Q = L 1 2 K 3 4 Find the marginal product of labor (MPL),...
Consider the following production function  q = K2 + L2. Does this production function exhibit constant, increasing...
Consider the following production function  q = K2 + L2. Does this production function exhibit constant, increasing or decreasing returns to scale?) Find an expression for the marginal rate of technical substitution. Does this production function exhibit diminishing marginal rate of technical substitution? Explain
A firm’s production function is Q(L,K) = K^1/2 + L. The firm faces a price of...
A firm’s production function is Q(L,K) = K^1/2 + L. The firm faces a price of labor, w, and a price of capital services, r. a. Derive the long-run input demand functions for L and K, assuming an interior solution. If the firm must produce 100 units of output, what must be true of the relative price of labor in terms of capital (i.e. w/r) in order for the firm to use a positive amount of labor? Graphically depict this...
Consider the following function: q = 9LK + 6L^2 - (1/3)L^3 Given the following expression for...
Consider the following function: q = 9LK + 6L^2 - (1/3)L^3 Given the following expression for the marginal productivity of each input: MPL = 9K + 12L - L^2 and MPK = 9L Assuming Capital is plotted on the vertical axis and labor is plotted on the horizontal axis, determine the value of the marginal rate of technical substitution when K=20 and L =10. (Round your answer up to two decimal places and include the proper sign.) MRTS= ___________
Given the Cobb-Douglas production function q = 2K 1 4 L 3 4 , the marginal...
Given the Cobb-Douglas production function q = 2K 1 4 L 3 4 , the marginal product of labor is: 3 2K 1 4 L 1 4 and the marginal product of capital is: 1 2K 3 4 L 3 4 . A) What is the marginal rate of technical substitution (RTS)? B) If the rental rate of capital (v) is $10 and the wage rate (w) is $30 what is the necessary condition for cost-minimization? (Your answer should be...
A firm’s production is represented by the following Cobb-Douglas function: ? = ?^2/3?^1/3. The rental rate,...
A firm’s production is represented by the following Cobb-Douglas function: ? = ?^2/3?^1/3. The rental rate, r, of capital is given by $200 and the price of labor is $100. a) For a given level of output, what should be the ratio of capital to labor in order to minimize costs? b) How much capital and labor should be used to produce those 300 units? c) What is the minimum cost of producing 300 units? d) What is the short...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT