1) Consider a company that outputs 1,000 doohickies. The company's long-runproduction function is: q= KL where q is the number of doohickiesproduced, K is the quantity of capital rented, and L is the quantity of laborhired.MP2- () ³and MP3- (+/-)²=The cost function is C=4K+L where C is the total costa. (10 pts) What ratio of capital to labor minimizes total costs?b. (10 pts) How much capital and labor are needed to produce 1,000doohickies? How much will these inputs cost them?

1) Consider a company that outputs 1,000 doohickies. The company's long-run production function is: q= KL where q is the number of doohickies produced, K is the quantity of capital rented, and L is the quantity of labor hired. MP -()* and MP -(-) The cost function is C= 4K+L where C is the total cost

1) Consider a company that outputs 1,000 doohickies. The company's long-run production function is: q= KL where q is the number of doohickies produced, K is the quantity of capital rented, and L is the quantity of labor hired. MP -()* and MP -(-) The cost function is C= 4K+L where C is the total cost

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

a. A firm's long-run total cost can be written as LTC = 3000Q - 50Q2 + (1/3)Q3 and its long-run marginal cost by LMC = 3000 - 100Q + Q2. Find the range over which the firm will experience economies of scale. Explain your answer. b. A firm has a production function of Q = K * L + L, where the marginal product of labor is MPL = K + 1 and the marginal product of capital is MPK = L. The wage rate (W) is $100 per worker and the rental price (R) is $100 per unit of capital. In the short-run, capital (K) is fixed at 4. Find the minimum total cost of production in the short- and long-run if the firm produces 100 units of output.
Production Functions and Cost Functions in the short run and in the long run Consider the production function Q=KL. The firm needs to produce 64 units of output. The price of capital is R=$16 and the price of labor is W=$4 a. In the short run, the firm's capital is fixed at K=16. How much labor will it use? What is its short run total cost? Hint: Solve it for a generic Q and plug Q=64 only at the very end b. Find the firm's short run total cost, average total cost, and marginal cost curves. Hint: If you are trying to find cost curves, Q is unknown. c. Set up a Lagrangian to find the firm's optimal inputs in.
Suppose w= 1 and r= 3. Solve the cost minimization problem to find L*(q) and K*(q). Then find the cost function C(q).
Suppose a firm with a production function given by Q = K0.4L0.6 produces 100 units of output. The firm pays a wage of $20 per units and pays a rental rate of capital of $40 per unit. (Note: MPL = 0.6K0.4L-0.4 and MPK = 0.4K-0.6L0.6 ) What is the minimum cost of producing 100 units of output?
A firm’s production is represented by the following function: Q = L1/4 K3/4 . The rental rate of capital (r) is $40 and the wage rate (w) is $12.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 400 units of output? What is the total cost?c. What is the short run total cost if output is decreased to 300 units?d. How would the capital labor choice and total cost change in the long run?e. Would the firm prefer to relocate if input prices are r = 60 and w = 8 at an alternativelocation assuming relocation is costless?
solve this one
Explain the relationship between the production function and the average costs and marginal costs curve of a firm.
1. Suppose the total-cost function for a firm is given by C = qw 1/4 3/4 a. Use Shephard's lemma to compute the (constant output) demand functions for each input, k and 1. b. Calculate the average cost and marginal cost. c. Describe the returns to scale for the underlying production function for q.
The following equation represents the cost structure of a firm: C= 10 + 3q. The average cost of production is
A firm has the following Cobb-Douglas production function: q=(L^α)(K^1-α)0<α < 1 is a parameter. Suppose in the short run K = 1. The rental rate of a unit of K is $10, and the wage rate of a unit of L is $20.(a) Derive the marginal cost of the firm (expressed in terms of α and q).(b) Derive the average variable cost of the firm (expressed in terms of α and q).(c) Derive the cost function of the firm.