Question: 2. Cost Minimization The production function for a product is given by q = K1/2L1/4 where K is capital, L is labor and q is

2. Cost Minimization The production function for a product is given by q = K1/2L1/4 where K is capital, L is labor and q is output.

a) Find the marginal products of labor and capital.

b) Is the marginal product of labor increasing or decreasing with labor? Is the marginal product of capital increasing or decreasing with capital? (Show your work to get credit. Just answering increasing or decreasing will not earn you any points)

c) Using your answers to part a) find the marginal rate of technical substitution between labor and capital.

d) Denote the wage of labor by w and the rental of capital by r. What is the cost minimization condition for a firm? Show it diagrammatically.

e) Now suppose w = 20 and r = 80. What is the minimum cost of producing q = 100. (You must show your work by clearly writing the equations that you use to derive the cost minimizing levels of L and K.)

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Economics Questions!

I. Increasing returns to scale in production means A) more than 10% as much of all inputs are required to increase output 10%. B) less than 3 times as much of all inputs are required to increase...

4. The production function for a product is given by q = 100KL, where K = capital and L = labour). The marginal products of labour and capital are; MPL = 100K and MPK = 100L. Assume, that the...

2. (12 points) The production function for a firm is given by Q = 311/3, where q denotes finished output and L denotes hours of labor input. The firm is a price-taker both for the final product...

2. The production function for a product is given by q = lKL. If the price of capital is $120 per day and the price of labor $30 per day, what is the minimum cost of producing 1000 units of output

1.2. The production function for a product is given by q = 100KL. If the price of capital is $120 per day and the price of labor $30 per day, what is the minimum cost of producing 1000 units of...

Suppose the production function for a product is given by q = 100KL. If the price of capital is $81 per clar,r and the price of labor is $27 dollars per day, what is the minimum cost of producing 900...

The production function for a product is given by q = 100KL. If the price of capital is $120 per day and the price of labor $30 per day, what is the minimum cost of producing 1000 units of output?

The production function of a product is given by q is equal to 100 KL. If the price of capital is ksh 150 per day and the price of labor is ksh 50 per day, calculate the cost of producing 1000units...

=+2. The production function for a product is given by q = 100KL. If the price of capital is $120 per day and the price of labor $30 per day,

I. Which of the following is correct? a) The pivot of the budget line shows the substitution effect while a slope gives the income effect. b) The pivot of the budget line shows the substitution...

An ideal Stirling engine using helium as the working fluid operates between temperature limits of 300 and 2000 K and pressure limits of 150 kPa and 3 MPa. Assuming the mass of the helium used in the...

draw 1- zygotic meiosis 2- gametic meiosis 3- sporic meiosis (alternation of generation) for each , note the organisms that use it .

What is DoS?

SIMAD UNIVERSITY Class: BACC25 Subject: Islamic Accounting Instructions: a) Follow The Instructions. Midterm Exam Instructor: All Ibrahim Date: 6-4-2022 b) You Have 1.5 Hrs. To Complete This Test. c)...

3. How can diversity be increased in an organisation without alienating people?

explain the concept of strategy formulation

describe what strategy is, including the different levels of strategy, and how corporate strategy affects HR strategy