Derive the marginal product functions

Assignment Help Microeconomics
Reference no: EM13562

1. Consider the production function:

661_Derive the marginal product functions.png

where Q is total output, K is the amount of capital used, and L is the amount of labor used.

a. Derive the marginal product functions for both K and L.

b. In the short run, with K fixed, does this production function exhibit diminishing marginal returns to labor?

c. Demonstrate whether or not this production function generates convex isoquants.

d. Demonstrate that the  production function exhibits constant returns to scale.

2. True or False, Explain:  In the short run, when total product is rising, the marginal product of labor must be increasing.

3. Consider a short run production function where K is fixed and L is variable.  Output rises from zero at a constant rate up until 10 units of L are used.  Beyond that, output rises at a decreasing rate up until 30 units of L are used.  Using more than 30 units of L causes output to decline.

a. Diagram the short run total product function.

b. Diagram the marginal product and average product of labor functions.

4. Can a production function be consistent with the law of diminishing marginal returns and increasing returns to scale?  Explain why or why not.

5. A firm's production function is given by 184_Derive the marginal product functions1.png.  Assume w = $20 and r=$10.

a. Derive the firm's demand functions for K and L .

b. Derive the long run total, average, and marginal cost functions. 

6. A firm's production function is given by 1327_Derive the marginal product functions2.png.  Assume w = $27, r = $18, and K is fixed at 3 units.

a. Derive the firm's short run demand for L.  

b. Derive the short run total cost (SRTC) function. 

c. Derive the SRMC, SRAVC, and SRATC functions. 

7. Generally, the cost minimizing combination of K and L to produce any level of output occurs where:

 

219_Derive the marginal product functions3.png

Fully explain why.   

8. Suppose a firm adopted a new capital saving technological innovation.  How would this affect the firm's long run expansion path.  Explain. 

9. True or False, Explain:  Increasing returns to scale implies that a firm can increase its long run output while reducing its long run total costs of production.   

10. Suppose that the total cost of providing satellite television services is given by:

1245_Derive the marginal product functions4.png

where Q1 and Q2 are the number of households that subscribe to a sports channel and movie channel, respectively.  Does the provision of satellite television services exhibit economies of scope?

Reference no: EM13562

Reviews

Write a Review

 

Microeconomics Questions & Answers

  Failure of the super committee is good thing for economy

Some commentators have argued that the failure of the “Super committee” is good thing for the economy?  Do you agree?

  Turning to a market economy

Developing countries in the "Global South" turned to socialism in the past as a means to solve their economic problems.

  Long-term growth, international trade & globalization

Long-term Growth, International Trade & Globalization:- This question deals with concepts such as long-term growth, international trade and globalization. Questions related to trade deficit, trade surplus, gains from trade, an international trade sce..

  Fixed cost and vairiable cost

Questions:  :   Which of the following are likely to be fixed costs and which variable costs for a chocolate factory over the course of a month?  Explain your choice.

  European monetary union (emu) in crisis

"Does the economic bailout of Spain and Greece spell the beginning of the end for the European Monetary Union (EMU)?"

  Article review question

Article Review Question: Read the following excerpts from the article "Fruit, veg costs surge' by Todd, Dagwell, published in the Herald on January 25th 2011 and answer questions below:

  Impact of external costs on resource allocation

Explain the impact of external costs and external benefits on resource allocation;  Why are public goods not produced in sufficient quantities by private markets?  Which of the following are examples of public goods (or services)? Delete the incorrec..

  Problem - total cost, average cost, marginal cost

Problem - Total Cost, Average Cost, Marginal Cost: -  Complete the following table of costs for a firm.  (Note: enter the figures in the  MC   column  between  outputs of  0 and 1, 1 and 2, 2 and 3, etc.)

  Linear demand function

Demand estimation and forecasting and income elasticity of demand

  Review the business cycle

The Business Cycle is the short-term fluctuations in the economy relative to the long-term trend in output; the recurring and fluctuating levels of the GDP growth rate over time.

  Evolution of the price of gold and silver

This document shows the uses supply and demand model to explain the evolution of the price of gold and silver.

  Regression modeling

Developing a regression model with Sample Regression Model

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