Derive the expressions of marginal product

Assignment Help Microeconomics
Reference no: EM13872412

1. Explain following terms:

Production function, Marginal product, Isoquant curve, TRS, Returns to scale, Isoprofit line, Isocost line

2. For each of following production functions comment on the ability to substitute capital for labor. Note that Q, K, and L denote output, capital, and labor respectively.

A: Q = K + L
B: Q = K0.5 L0.5
C: Q = min{K, L}

3. Justify whether the following statement is true or false. "If the production function is y = f(x1, x2) = x12x22 , then it exhibits constant returns to scale."

4. Justify whether the following statement is true or false. "If the value of the marginal product of labor exceeds the wage rate, then a competitive, profit maximizing firm would want to hire less labor."

Problem 1:

A profit-maximizing competitive firm uses just one input, x, to produce output y. Its production function is:

y = 8x1/2

The price of output is 40$ each unit and the factor price is 8$ each unit.

a. Find profit-maximizing output and the amount of the factor that the firm demands.

b. Find also the maximum profits. (Hint: the marginal product of the factor is 4x-1/2.)

Problem 2:

Weeding a vegetable patch only requires labour as an input. The output of such an activity is the number of square meters weeded per day, defined as Y. The relationship between Y and the amount of labour L is:

Y = 20L1/2

a. Draw this relationship on a graph and label it.

b. Is the marginal product of labour always positive? Does this relationship obey the "law" of diminishing marginal returns?

Problem 3:

A farmer uses two inputs (labour:L, and Fertilizer:F) to produce his only output (corn: C). His production function is : C= f(L,F) = 2L1/2F1/2.

a- Derive the expressions of marginal product of labour MPL and marginal product of fertilizer MPF.

b- Use your answers in (a) to check if the decreasing marginal return law is verified.

c- Let WL be the wage per hour and WF the price per one kg of fertilizer. What is the long run cost-minimization condition for this farmer given his technology of production described above? (4 points)

d- What would be the ratio of labour to fertilizer knowing that WL = $8 and WF = $4
e- What are the optimal amounts of labour and fertilizer that this farmer should use to produce 1kg of corn?

f- What would be the cost of producing 1kg of corn?

g- In general, given his production function, if the farmer doubles the amount of the inputs by how much would the output be multiplied? What does this tell you about the returns to scale?

h- Is the answer in (g) in contradiction with the answers found in (b)? Clearly explain.

Verified Expert

Reference no: EM13872412

Demand for courses-increase their fees elastic or inelastic

Is demand for courses at the universities that did not increase their fees elastic or inelastic with respect to universities that did increase their fees? What is the import

How economy is experiencing a sharp and prolonged trend

Suppose that you are a member of the Board of Governors of the Federal Reserve System. The economy is experiencing a sharp and prolonged inflationary trend. What changes in

Marketable securities portfolio

Ralph, a treasurer for Ma nd M products, Inc., recently updated his firm's short-term cash forecast only to discover that the firm will suffer a cash shortabe of $15 million f

Discuss the steps that would have helped a negotiator

Discuss the steps that would have helped a negotiator / manager like Brian Epstein to prevent media and entertainment industries from taking advantage of his / her lack of

Lower the price of vcr

1. Which of the following would not tend to lower the price of VCR? a. Decreasing price of DVD players. b. Increasing price of video cassettes. c. Improvements in VCR producti

The annual depreciation on the equipment

An oil refinery has decided to purchase some new drilling equipment for $550,000. The equipment will be kept for 10 years before being sold. The estimated MV (SV) for deprecia

Advantages of herfindahl index over concentration ratios

What are the advantages of the Herfindahl index over concentration ratios in measuring degrees of concentration in an industry? (b) What is the disadvantage of both?

Assume that the market for wheat is perfect competitive

Assume that the market for wheat is perfect competitive, with demand curve P = 5000 - 0.01QD and a supply curve P = 1+0.1QS. Each identical wheat producer has a total cost c

Reviews

Write a Review

 
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd