McPeak Name:____________________________
PPA 723 November 9, 2004
Quiz 2
1) Returns to scale and economies of scale. (2 points)
a. My current level of production is 7 units. If I double my input bundle and my output level becomes 14 units, do I have increasing, constant, or decreasing returns to scale in production? Why?
b. Is a natural monopoly characterized by economies of scale or diseconomies of scale over the feasible range of output? Explain your answer.
c. Define diminishing marginal returns and decreasing returns to scale.
2) Cost issues. (2 points)
a. If there are fixed costs in production, is the average variable cost curve above or below the average cost curve? Why?
b. If marginal cost is below average cost at a given level of output, will average cost rise or fall when we move to the next level of output? Why?
c. Illustrate using a specific firm’s marginal cost and average cost curves how an increase in input costs leads to a shift in the firm’s supply curve.
3) Production and cost functions. (2 points)
a. You are given the following information. Calculate marginal product for each change in input level.
|
Input level |
Output level |
Marginal Product |
|
0 |
0 |
NA |
|
1 |
110 |
|
|
2 |
210 |
|
|
3 |
300 |
|
|
4 |
380 |
|
|
5 |
450 |
|
|
6 |
510 |
|
|
7 |
560 |
|
|
8 |
600 |
|
|
9 |
630 |
|
b. Given your findings on marginal product in (a), is the average product curve: downward sloping over all input levels, upward sloping over all input levels, upward sloping for some input levels and downward sloping for other input levels?
c. If the cost of the input is $100 per unit, calculate the cost of producing each level of output, and the marginal cost for changing the output level.
|
Input level |
Output level |
Cost of producing |
Marginal Cost |
|
0 |
0 |
0 |
NA |
|
1 |
10 |
|
|
|
2 |
22 |
|
|
|
3 |
31 |
|
|
|
4 |
40 |
|
|
|
5 |
48 |
|
|
|
6 |
55 |
|
|
|
7 |
61 |
|
|
|
8 |
66 |
|
|
|
9 |
70 |
|
|
4) Production functions. (2 points).
a. Define in words or using a formula the marginal product of labor when labor is an input in a production function.
b. Define in words or using a formula the average product of labor if labor is an input in a production function.
c. Draw a sample production function and illustrate for a given input level:
· Point one representing an output level that is not technologically efficient given that input level;
· Point two representing an output level that is technologically efficient given that input level;
· And point three representing an output level that is not technologically feasible given that input level.
5) You know that the inverse demand curve is defined by the following function: P=45-Q and costs are defined by 5*Q (so you know MC is 5 for all possible levels of Q). (2 points)
a. Use the bisection rule to define the marginal revenue curve
b. Draw the marginal revenue curve, the demand curve, and the marginal cost curve on a single graph.
c. What level of Q should the monopolist produce at?
d. What is the implied price?
e. What is the implied profit?
6) Continue with the information in the previous question, so you are still working with the information that P=45-Q, and MC =5. (2 points)
a. If this were to become a perfectly competitive market for some reason, what would the market price and quantity in the market be if all firms had identical cost structures to the monopoly firm and the demand curve was unchanged?
b. Show the competitive case in comparison to the monopoly case on a single graph.
c. Calculate the value of the following areas under the competitive and the monopoly structure.
|
|
Competitive Market Structure |
Monopoly Market Structure |
|
Consumer Surplus |
|
|
|
Producer Surplus |
|
|
|
Dead Weight Loss |
|
|
|
Total Social Welfare |
|
|
7) Necessary and sufficient conditions. Circle the correct answer. (2 points)
|
Condition One |
Condition Two |
To identify condition
two as true, is condition one necessary or sufficient? |
|
A firm uses an input in production. |
Production is technologically efficient with respect to this input. |
Necessary Sufficient |
|
An input bundle is economically efficient. |
The input bundle is technologically efficient. |
Necessary Sufficient |
|
The market is a perfectly competitive market |
Price taking behavior by producers |
Necessary Sufficient |
|
The bundle |
The point defined by the bundle K, L is on the expansion path.. |
Necessary Sufficient |
|
Average Cost upward sloping at a given level of output |
Marginal cost > average cost at that level of output. |
Necessary Sufficient |
|
MR (q*) = MC (q*) |
The profit maximizing level of production is q* |
Necessary Sufficient |
|
Felix is a cat |
Felix hates baths |
Necessary Sufficient |
|
Output less than doubles when inputs double |
The firm is experiencing increasing returns to scale |
Necessary Sufficient |
satisfies 
8) Assume the rental rate of capital is 4 and the wage rate is 8. (2 points)
a. Draw an isocost curve for a total cost level of 80.
b. If the marginal product of labor is 2, what is the marginal product of capital at an economically efficient point? Why?
c. What is the technical name for the slope of an isoquant?
9) Complete the following table. (2 points)
|
a) Quantity of Output |
Fixed Cost |
Total Cost |
Average Cost |
Marginal Cost |
Variable Cost |
Average Variable Cost |
|
0 |
5 |
5 |
------------ |
--------- |
----------- |
----------- |
|
1 |
|
|
|
15 |
|
|
|
2 |
|
34 |
|
|
|
|
|
3 |
|
49 |
|
|
|
|
|
4 |
|
|
|
|
|
15 |
|
5 |
|
82 |
|
|
|
|
|
6 |
|
|
|
|
95 |
|
|
7 |
|
|
17 |
|
|
|
|
8 |
|
139 |
|
|
|
|
b. If the market price for the output produced is 17 and the market structure is competitive, what level of output is the profit maximizing level of output? Why?
c. Is the information presented in (a) long run or short run cost information? Why?
10) Isoquants. (2 points)
a. Define an isoquant.
b. Is the slope of an isoquant positive or negative. Why?
c. Draw an isoquant illustrating a production setting in which the inputs are easily substituted.