The economy is populated by two firms. One firm produces cars (c), the other produces beans (b). The production function of each firm i = {c, b} is Y; K L-4. Cars are capital intensive, hence a > an. The price of cars is pe and the price of beans is po. Firms take all prices as given. The unit cost of labor is w and the unit cost of capital is r. The total amount of labor and capital in the economy are, respectively, L and K. 1. Write down the optimality condition for capital and labor of each firm 2. Derive the capital-to-labor ratio of each firm 3. Define an equilibrium for this economy 4. The quantities used by the firm producing cars as a fraction of the total quantities in the economy are K. = nKK and Le = n1,L, for some values 0 < nK <1 and 0 < nL < 1. Use the labor and capital market clearing to find analogous expressions for K, and Lp. How many equilibrium condi- tions are you left with? What are equilibrium values you are left to solve for?

The economy is populated by two firms. One firm produces cars (c), the other produces beans (b). The production function of each firm i = {c, b} is Y; K L-4. Cars are capital intensive, hence a > an. The price of cars is pe and the price of beans is po. Firms take all prices as given. The unit cost of labor is w and the unit cost of capital is r. The total amount of labor and capital in the economy are, respectively, L and K. 1. Write down the optimality condition for capital and labor of each firm 2. Derive the capital-to-labor ratio of each firm 3. Define an equilibrium for this economy 4. The quantities used by the firm producing cars as a fraction of the total quantities in the economy are K. = nKK and Le = n1,L, for some values 0 < nK <1 and 0 < nL < 1. Use the labor and capital market clearing to find analogous expressions for K, and Lp. How many equilibrium condi- tions are you left with? What are equilibrium values you are left to solve for?

Exploring Economics

8th Edition

ISBN:9781544336329

Author:Robert L. Sexton

Publisher:Robert L. Sexton

Chapter11: The Firm: Production And Costs

Section: Chapter Questions

Problem 21P

See similar textbooks

Similar questions

We expect the marginal cost to increase as this firm produces more computers. But when the firm shifts from producing 1 to 2 computers, marginal cost falls. Why?
1. Micky's auto mechanic shop has a daily total cost represented by: C = 100 + 4q + 4q². Shop's marginal cost is given by: MC = 4 + 8q, where q is the number of repaired cars. a. Derive an expression for average cost. b. Find the quantity range where the shop experiences the economies scale (Hint: scale economy index is given by: S = . c. At what production level are scale economies exhausted?
At a current level of production of 10,000 per day in its Garner plant, the marginal cost of producing a Jess Jones Sausage is 50 cents. If the average cost of production is 40 cents, at that level of production, Select one: a. the average cost of production will increase if output is increased above 10,000 sausages per day. O b. the average cost of production will remain 40 cents if output is increased above 10,000 sausages per day. c. the average cost of production will decline if output is increased above 10,000 sausages per day. O d. the average fixed cost of production will increase if output is increased above 10,000 sausages per day.
2. The Acme Anvil Company's output is given by the Cobb-Douglas Production function P = 60L2/3K1/3, where P is the number of anvils produced when L is the amount spent on labor and K is the amount spent on capital. a. What is the production if L = 150 and K = 150? b. Find the marginal productivities. c. Evaluate the marginal productivities with L = 150 and K = 150. d. Interpret the meanings of the marginal productivities found in part c. e. If their budget is $300 then there is a constraint L+ K = 300. Use Lagrange multipliers (2) to find the values of L and K that will maximize production and find the maximum production f. Find 2. 12| is called the marginal productivity of money and will give the number additional units produced for each dollar increase in the budget. Interpret 2 for this problem. Only need paVAS e and fl
If this firm is producing.... please solve
The firm will maximize profits by producing____ units of outputs (Enter your response as an integer.)
QUESTION 6 Easy-toothy is a price-taking producer of tooth fairy's sling bags (these are bags for tooth fairies to carry coins and teeth). The following table depicts Easy-toothy's total cost of producing different quantities of tooth fairy's sling bags. Output level Total Cost ($) 0 1 2 13 4 5 10 0000 13 8 00 X 30 50 Which of the following values of x is consistent with Easy-toothy to optimally produce 3 units of output when the price of tooth fairy's sling bags is $10/unit? 17 20 27 There is insufficient information to determine.
The Acme Anvil Company's output is given by the Cobb-Douglas Production function P = 60L2/3 K1/3, where P is the number of anvils produced when Lis the amount spent on labor and K is the amount spent on capital. a. What is the production if L = 150 and K = 150? b. Find the marginal productivities. C. Evaluate the marginal productivities with L = 150 and K = 150. d. Interpret the meanings of the marginal productivities found in part c. e. If their budget is $300 then there is a constraint L+ K = 300. Use Lagrange multipliers (2) to find the values of L and K that will maximize production and find the maximum production f. Find 2. 12| is called the marginal productivity of money and will give the number additional units produced for each dollar increase in the budget. Interpret 2 for this problem. MacBook Pro urses/34419/files/5014304?wrap=1
IV. Will can produce a higher grade, Gw, on an upcoming economic exam by studying. His production function depends on the number of hours he studies marginal analysis problems, A, and the number of hours he studies supply and demand problems, R. Specifically, Gw = 2.5A0.36R 0.64. His roommate David's grade production function is G) = 2.5A0.25R0.75 a. What is Will's marginal productivity from studying supply and demand problems? What is David's? b. What is Will's marginal rate of technical substitution between studying the two types of problems? What is David's?
A firm’s cost curves are given in the following table. q TC TFC TVC AVC ATC MC Revenue Profit 0 RO100 RO100 1 140 100 2 160 100 3 170 100 4 182 100 5 195 100 6 220 100 7 250 100 8 290 100 9 340 100 10 400 100 Complete the table. Graph AVC, ATC and MC on the same graph. What is the relationship between the MC curve and the ATC and between MC and AVC? Suppose the market price is RO 60, how much will the firm products in the short run? How much are the total profits?
We expect the marginal cost to increase as this firm produces more computers. But when the firm shifts from producing 1 to 2 computers, marginal cost falls. What might explain this?
What are transaction costs? How do transaction costs affect the boundaries of a firm?