STUDY GUIDE (Winter 1999)

Chapter 6: PRODUCTION

1. Production function and isoquants

2. Production with 1 variable input and optimal use of an input

3. Production in the long-run

4. Least cost production and the optimal employment of inputs

5. Cobb-Douglas and other production functions

6. Multiple plants

Reading: All

Problems: 1,3,5,6,8,10-13

WHAT YOU SHOULD BE ABLE TO DO

1. Understand and work with short-run relationships through tables, graphs or equations: TP, MP, AP, and MRP

2. Determine the optimal use of a variable input

3. Understand and work with 2-variable or long-run concepts including

-isoquants and budget line

-MRTS

-returns to scale

4. Deal with optimum employment of inputs in problems with output maximization or cost minimization

5. Understand properties of Cobb-Douglas production functions

6. Work with multiplant and similar problems involving equimarginal principle

EXAMPLE

Suppose Q = 100L0.5K0.4

a. How much output will be produced if L=5 and K=5.

b. Fill in the values for the following for Q, APL, and MPL (using finite changes for MPL assuming K=5).
 
Q L APL MPL MRPL
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c. Determine the equations for the marginal product of labor and average product of labor.

d. Is the production function consistent with the Law of Diminishing Returns to labor? To capital (if capital is not fixed)?

e. If labor costs $10 per unit and the product sells at a constant price of $25, determine the optimal number of units of labor. Also fill in the column for MRPL based on your column for MPL. Explain why it is clear from the table that more than 5 units of labor will be used.

f. Assuming that K is no longer fixed, explain whether the production function has constant, increasing, or decreasing returns to scale. What is the output elasticity?

g. The firm desires to produce 400 units of output. Determine the values of K corresponding to the following values of L.
 
L K MRTSLK MRTSLK (Calculus)
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5      
h. Is the isoquant consistent with the Law of Diminishing Marginal Rate of Technical Substitution? Plot it on a graph. Fill in the values for MRTS using both finite changes and the calculus method.

i. Assume that L costs $10 per unit and K costs $20 per unit. Determine the equation for the isocost curve with a budget of $500. Draw the graph noting the vertical (K) and horizontal (L) intercept values. What is the slope?

J. Determine the maximum output that can be produced with a budget of $500.

K. Determine the minimum cost of producing 1000 units of output.

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