ZuoTi.Pro
Question

Consider the Cobb-Douglas production function Q = 6 L^½ K^½ and cost function C = 3L...

Consider the Cobb-Douglas production function Q = 6 L^½ K^½ and cost function C = 3L + 12K.

a. Optimize labor usage in the short run if the firm has 9 units of capital and the product price is $3.

b. Show how you can calculate the short run average total cost for this level of labor usage?

c. Determine “MP per dollar” for each input and explain what the comparative numbers tell in terms of the amount of labor and capital being used in the short run.

d. Optimize for both inputs L & K for a long-run output constraint of Q = 192 units and prove that the average total cost is lower after long-run optimization.

business   economics   
0 0
Add a comment Improve this question Transcribed image text
Next > < Previous
Sort answers by oldest

Homework Answers

Answer #1

0 0
Add a comment
Know the answer?
Add Answer to:
Consider the Cobb-Douglas production function Q = 6 L^½ K^½ and cost function C = 3L...
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. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions

  • A firm has a Cobb-Douglas production function q = AKL, where K denotes capital, L is...

    A firm has a Cobb-Douglas production function q = AKL, where K denotes capital, L is labor, and A, a, b, are constants. ginal returns to labor in the short run if its production function is 1. Sketch an isoquant line, write a mathematical formula for its slope, and provide an interpretation for its meaning. 2. On a separate graph, draw an isocost line, write a mathematical formula for its slope, and provide an interpretation for its meaning. 3. On...

  • A firm has a Cobb-Douglas production function of Q = K^(0.25) L^(0.75) (a) Does this production...

    A firm has a Cobb-Douglas production function of Q = K^(0.25) L^(0.75) (a) Does this production technology exhibit increasing, constant, or decreasing returns to scale? (b) Suppose that the rental rate of capital is r = 1, the wage rate is w = 1, and the ?rm wants to produce Q = 3. In the long-run, what combination of L and K should they use? (It would be good to practice doing this with the Lagrangian, even if you can...

  • Consider the following Cobb-Douglas production function for a firm that uses labor hours (L), capital (K),...

    Consider the following Cobb-Douglas production function for a firm that uses labor hours (L), capital (K), and energy (E) as inputs: Q = (0.0012L^0.45)(K^0.3)(E^0.2) Determine the labor, capital and energy production elasticities. Suppose that worker hours are increased by 2 percent holding other inputs constant.  What would be the resulting percentage change in output? Suppose that capital is decreased by 3 percent holding other inputs constant.  What would be the resulting percentage change in output? What type of returns to scale appears...

  • Suppose a Cobb-Douglas Production function is given by the following: where L is units of labor, ...

    Suppose a Cobb-Douglas Production function is given by the following: where L is units of labor, K is units of capital, and P(L, K) is total units that can be produced with this labor/capital combination. Suppose each unit of labor costs $300 and each unit of capital costs $1,200. Further suppose a total of $120,000 is available to be invested in labor and capital (combined). A) How many units of labor and capital should be "purchased" to maximize production subject...

  • 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,...

  • 2. For the following Cobb-Douglas production function, q = f(L,K) = _0.45 0.7 a. Derive expressions...

    2. For the following Cobb-Douglas production function, q = f(L,K) = _0.45 0.7 a. Derive expressions for marginal product of labor and marginal product of capital, MP, and MPK. b. Derive the expression for marginal rate of technical substitution, MRTS. C. Does this production function display constant, increasing, or decreasing returns to scale? Why? d. By how much would output increase if the firm increased each input by 50%?

  • 6. a) Consider the following Cobb-Douglas production function: Q AK°L where Q output, K labour, L...

    6. a) Consider the following Cobb-Douglas production function: Q AK°L where Q output, K labour, L labour Express the above function in a logarithmic form

  • suppose a firm has a cobb-douglas weekly production function q=f(l,k)=25l^.5k^.5, where l is the number of...

    suppose a firm has a cobb-douglas weekly production function q=f(l,k)=25l^.5k^.5, where l is the number of workers and k is units of capital.mrtslk is k/l. the wage rate is $900 per week, and a unit of capital costs $400 per week. assuming no fixed cost, what is the firm's total cost of production if it uses least-cost input combination to produce 675 units of output?

  • A firm production is represented by the following Cobb-Douglas function: Q=K1/4L3/4 The rental rate, r, of...

    A firm production is represented by the following Cobb-Douglas function: Q=K1/4L3/4 The rental rate, r, of capital is given by $100 and the price of labor w is $200. 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 300 units? c. What is the minimum cost of producing 300 units? d. What is the additional cost of...

  • A “Cobb–Douglas” production function relates production (Q) to factors of production, capital (K), labor (L), and...

    A “Cobb–Douglas” production function relates production (Q) to factors of production, capital (K), labor (L), and raw materials (M), and an error term u using the equation: ? = ???1??2M?3? ?, where ?, ?1, ?2, and ?3 are production parameters. a) Suppose that you have data on production and the factors of production from a random sample of firms with the same Cobb–Douglas production function. How would you propose to use OLS regression analysis to estimate the above production parameters,...

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT