Purchase Solution

Production function: Average and Marginal Product of Labor

Not what you're looking for?

Ask Custom Question

A firm can manufacture a product according to the production function
Q = F(K, L) = K^(3/4) L^(1/4)

a) Calculate the average product of labor, APL, when the level of capital is fixed at 16 units and the firm uses 16 units of labor. How does the average product of labor change when the firm uses 81 units of labor?

b) Find an expression for the marginal product of labor, MPL, when the amount of capital is fixed at 16 units. Then, illustrate that the marginal product of labor depends on the amount of labor hired by calculating the marginal product of labor for 16 and 81 units of labor.

c) Suppose capital is fixed at 16 units. If the firm can sell its output at a price of $100 per unit and can hire labor at $25 per unit, how many units of labor should the firm hire in order to maximize profits?

Purchase this Solution
Solution Summary

The average product of labor and marginal product of labor are found under specific circumstances. Step-by-step computations are provided for each problem. Explanations are given for every formula used.

Solution Preview

A firm can manufacture a product according to the production function
Q = F(K, L) = K^(3/4) L^(1/4)

1 a)
Calculate the average product of labor, APL, when the level of capital is fixed at 81 units and the firm uses 16 units of labor.

Find the value of Q by using the production function

where the variables are defined as follows
Q = the level of output produced in the production process
K = quantity of capital
L = quantity of labor

Let the level of capital be K = 81
Let the number of units of labor be L = 16.
Then we ...

Solution provided by:
J Pye, MSc
Education
  • MSc, California State Polytechnic University, Pomona
  • MBA, University of California, Riverside
  • BSc, California State Polytechnic University, Pomona
  • BSc, California State Polytechnic University, Pomona
Recent Feedback
  • "Excellent work. Well explained."
  • "Can you kindly take a look at 647530 and 647531. Thanks"
  • "Thank you so very much. This is very well done and presented. I certainly appreciate your hard work. I am a novice at statistics and it is nice to know there are those out there who really do understand. Thanks again for an excellent posting. SPJ"
  • "GREAT JOB!!!"
  • "Hello, thank you for your answer for my probability question. However, I think you interpreted the second and third question differently than was meant, as the assumption still stands that a person still independently ranks the n options first. The probability I am after is the probability that this independently determined ranking then is equal to one of the p fixed rankings. Similarly for the third question, where the x people choose their ranking independently, and then I want the probability that for x people this is equal to one particular ranking. I was wondering if you could help me with this. "
Purchase this Solution
Free BrainMass Quizzes
Basics of Economics

Quiz will help you to review some basics of microeconomics and macroeconomics which are often not understood.

Economic Issues and Concepts

This quiz provides a review of the basic microeconomic concepts. Students can test their understanding of major economic issues.

Pricing Strategies

Discussion about various pricing techniques of profit-seeking firms.

Elementary Microeconomics

This quiz reviews the basic concept of supply and demand analysis.

Economics, Basic Concepts, Demand-Supply-Equilibrium

The quiz tests the basic concepts of demand, supply, and equilibrium in a free market.

View More Free Quizzes
Related BrainMass Solutions

  • Product functions - Total, average & marginal product

    In simple steps it shows how to write the three functions from the long run production function, calculate the point of maxima and calculate the total, average and marginal product for a specific labor level.

  • total output

    378090 Economic concepts are depicted The following is a hypothetical short-run production function: The following is a hypothetical short-run production function Hours of labor Total output Marginal product 0 ?

  • Production and cost analysis in the short and long run

    The Average Product of Labor is the output of an average worker, so it is Q/L, the Marginal Product of Labor is Q/L AP = 200,000/1000 = 200.

  • Determining the production parameters

    Solution describes the steps to calculate average product and marginal product in the given case. It also determines whether given production function exhibits increasing/decreasing/constant returns to scale.

  • computing marginal product and average product of labor

    Given three different production functions (linear, quadratic, cubic) I derive the marginal product of labor and the average product of labor. the results are then graphed and discussed.

  • Cubic Production Function

    449502 Questions about Cubic Production Function: What are the equations for total product, average product, and marginal product? When does marginal product of labor begin to diminish? What is average variable cost and marginal cost?

  • The marginal product of labor

    47421 Marginal product of labor & production function Does the marginal product of labor measure how output changes as the wage rate changes, or is it the average product of labor divided by the quantity of capital stock and can it be negative or is it

  • Average and Marginal Products, Diminishing Returns

    232252 Production Function - Average and Marginal Product Problem: The short run production function for a manufacturer of DVD drivers is as follows: Input of Labor (workers per week) Total output of DVD drivers 0

  • Production Function and Total Product of Labor

    180157 Production Function and Total Product of Labor See the attached file for further details. A firm's production function is given by: Q= Le^-0.2L Find the value of L which maximizes the TOTAL PRODUCT of labor.

View More Related Solutions