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Answers to Review Questions

Chapters 9-10

Chapter 9 The Firm and Its Constraints

(This is not done as JavaScript) 1. Students often confuse production functions and production-possibilities frontiers. They are different relationships, but they are related. The following exercise illustrates their relationship.

Suppose an economy has three units of capital and four units of labor. It must use these resources to produce the only two goods it uses: food and shelter. The technology possessed in this economy is shown in the following production functions:

Notice that if resources are fixed in amount and if they are used to produce food, they cannot be used to produce shelter. If, for example, two units of capital and two units of labor are used to produce food, then only one unit of capital and two units of labor will be available to produce shelter.

Complete the production-possibilities table for this economy:

The only two changes that alter a production-possibilities frontier are changes in technology or resources. Why?

To get different numbers in the production-possibilities table, either the numbers in the production functions must be different (a change in technology), or the pairings of boxes must be different (a change in resources.)

(This is not done as JavaScript) 2. Fill in the blanks:

Amount of Capital	Total Cost	Output	Total Revenue
20	$50,000	89	$55,000
22	$50,100	90	$55,300

a) Increasing capital by 1 increases costs by $50.
b) Increasing capital by 1 increases output by .5.
c) Increasing output by 1 increases revenue by $300.
d) Increasing output by 1 increases cost by $100.
e) Increasing capital by 1 increases revenue by $150.

3. Answer the same questions using the following table and the technical terms of economics:

Amount of Capital	Total Cost	Output	Total Revenue
109	$120,000	500	$130,000
111	123,000	505	134,000

f) Marginal resource cost of capital = $1500.
g) Marginal product of capital = 2.5.
h) Marginal revenue = $800.
i) Marginal cost = $600.
j) Marginal revenue product = $2000.

4. Fill in the blanks:

a) Marginal resource cost of capital = $10
b) Marginal product of capital = 2
c) Marginal revenue = $6
d) Marginal cost = 5
e) Marginal revenue product =$12

Chapter 10 Maximizing Profits

Exploring Profit

1. Some critics of capitalism have suggested that we need some way to measure the social responsibility of business. (Look at "corporate social responsibility" at wikipedia.com. Anyone who likes to talk about stakeholders rather than shareholders is an advocate of this position.) The response by some economists, such as Milton Friedman, (search for him on the internet--who was he and for what is he famous?) is that profit is as good a measure as we are likely to get of the social responsibility of business, at least if we have reasonably competitive markets. A firm that produces at a loss is socially irresponsible, while a firm that makes a profit is socially responsible. What is the argument behind this assertion, that is, why is a firm running a loss rather than a profit being socially irresponsible?

If a firm is running at a loss, it is transforming resources worth $100 into something worth less than $100. We do not want to reduce the value of resources. It is socially responsible to increase the value of these resources, and socially irresponsible to reduce their value. It is a simple argument that is not understood by a whole lot of people.

Every economists should be able to explain why profit can be considered a measure of social responsibility, Every economist also is aware of many problems of using profit for this purpose. Several later chapters of CyberEconomics are devoted to explaining these problems. But to get a head start, search the internet for the term "market failure" and explain how what you find weakens the case for using profit as a measure of social responsibility.

Answers will vary. However, once there is market failure, We will have situations in which firms can take resources worth $100 and transform them into something worth $200 and not be able to make a profit, or they may be able to take resources worth $100 and transform them into something worth only $50 and make a profit. So using profit as a measure of social responsibility is dangerous. But the alternatives are too.

Exploring Profit Maximizing Output

(now JavaScript) 2. Use the following table for the next four questions:

OUTPUT	TOTAL COST	MARGINAL REVENUE
1	$9.00	$8.00
2	$13.00	$8.00
3	$17.00	$8.00
4	$22.50	$8.00
5	$30.00	$8.00

a) What is the marginal cost of the third unit of output?
($17.00-$13.00)=$4.00

b) What is the average cost of four units of output?
$22.50/4 = $5.625

c) What is profit or loss when output is 4?
$32.00-$22.50 = $9.50

d) Where are profits maximized?
At an output of 5. Until then marginal revenue exceeds marginal cost.

3. The table of the reading (reproduced below) showed a seller maximizing profit at three units of output. Suppose that the government puts a price ceiling of $15 on this seller.

Computation of the Best Output for the Firm
(1) Output	(2) Total Cost	(3) Price	(4) Total Revenue	(5) Marginal Revenue	(6) Marginal Cost
0	10	--	--	--	--
1	20	18	$15	$15	10
2	31	17	$30	$15	11
3	43	16	$45	$15	12
4	56	15	$60	$15	13
5	70	14	$70	$10	14
6	85	13	$78	$8	15

a) Recompute the total revenue and marginal revenue columns of the table. (Hint: What is the highest price the seller can charge if it sells only one unit? If it sells six units? Be careful.)

b) What is the profit-maximizing level of output with the price ceiling?
4 (without price controls, the profit maximizing output was 3. The third one added $14 in revenue and $12 in cost. The fourth added $12 in revenue but $13 in cost, so was not worth producing.)

c) Using supply and demand curves, we showed that price ceilings reduced output. However, the price ceiling in this problem is not reducing output. What is going on? (Hint: Check the section on supply and demand for assumptions on the number of buyers and sellers needed for supply and demand curves.)

In supply and demand, we assumed that there were many sellers, and no one seller had any effect on price. In jargon, was assumed sellers were price takers. Here the seller is not a price taker. If he sells more, he must lower price. With different assumptions, we get different results. Price controls make this seller act more like a price taker.

4. a) Suppose there are 30 people in a room with the average age of 40 years. A 15-year-old boy walks in and the average age of the group becomes 40.5. Is this possible?
No. The average must decrease.

b) A firm is producing 30 units of output at an average cost of $40. Adding another unit will increase costs by $15 (this is the marginal cost) and the average cost will rise to $40.5. Is this possible?
No. The average must decrease.

c) If average cost is falling, what must be true of marginal cost?

It lies below the average.

5. The table in the reading (reproduced below) illustrates two different ways to compute the profit-maximizing position for a firm. The profit-maximizing firm will hire four units of labor and produce 31 units of output.

Computation of the Best Input Level for the Firm
(1) Marginal Revenue Product	(2) Marginal Resource Cost	(3) Labor	(4) Output	(5) Marginal Product	(6) Marginal Revenue	(7) Marginal Cost
--	--	0	0	--	--	--
$27.30	$10.00	1	13	13	$2.10	$.77
14.70	10.00	2	20	7	$2.10	1.43
12.60	10.00	3	26	6	$2.10	1.67
10.50	10.00	4	31	5	$2.10	2.00
8.40	10.00	5	35	4	$2.10	2.50

a) Suppose that there are fixed costs of $15.00 that must be paid to capital. (Recall that capital is held fixed at two units.) What will the profit of the firm be? (Hint: Compute the total revenue and total cost columns in the following table, and then subtract the latter from the former to find profit.)
We hire four labor and produce 31. Total revenue is 31*$2.10 or $65.10. Total cost is $40 for labor plus fixed costs of $15, or $55. Hence, total profit is $10.10.

b) What will happen to the profit-maximizing output if fixed costs are decreased to 10? If they are eliminated? (Hint: What will a change in fixed costs do to the marginals in the table?)
Fixed costs do not affect marginal costs. Hence, changing them does not alter the profit-maximizing output.

c) Suppose that the workers run the firm, and that they want to maximize profit per worker, not total profit. How much will they produce and how many workers will the firm hire, assuming that fixed costs are $15? (Hint: Compute the profit-per-worker column in the following table.)
Best for the worker-run factory would be an output of 2. Best for the profit-maximizing factory is 4. This example exposes a serious incentive problem with a system in which workers own enterprises. It was almost entirely ignored by those who advocated such systems. That advocacy seems to have diminished in recent decades, but sooner or later it will revive. Even bad ideas keep coming back.

 

Labor	Output	Total Revenue	Total Cost	Profit	Profit per Worker
0	0	$0	$15	-$15	--
1	13	27.30	25	2.30	2.30
2	20	42.00	35	7.00	3.50
3	26	54.60	45	9.60	3.20
4	31	65.10	55	10.10	2.525
5	35	73.50	65	8.50	1.70

(Comment: Before the fall of communism, Yugoslavia tried to implement a system of worker management. One problem that plagued them was high unemployment.)

6. Following are two tables that are similar to a table in the readings but with different numbers.

a) Complete the tables and find the profit-maximizing levels of output and labor.

(1) Marginal Revenue Product	(2) Marginal Resource Cost	(3) Labor	(4) Output	(5) Marginal Product	(6) Marginal Revenue	(7) Marginal Cost
$30.00	$9.00	1	10	10	$3	$.90
25.00	10.00	2	20	10	2.5	1.00
20.00	11.00	3	30	10	2	1.10
15.00	12.00	4	40	10	1.5	1.20
10.00	13.00	5	50	10	1.00	1.30

(1) Marginal Revenue Product	(2) Marginal Resource Cost	(3) Labor	(4) Output	(5) Marginal Product	(6) Marginal Revenue	(7) Marginal Cost
$8	3.00	.5	1	2	$4.00	$1.50
7	3.00	1.0	2	2	3.50	1.50
5	3.00	1.6	3	1.667	3.00	1.80
3.52	3.00	2.3	4	1.43	2.50	2.10
2.50	3.00	3.1	5	1.25	2.00	2.40

b) Compute the supply curve of labor that exists for the first table, and the demand curve for output that exists for the second table.

Amount of Labor	Wage	*****	Amount of Output	Price
1	$9.00		1	$4.00
2	9.50		2	3.75
3	10.00		3	3.50
4	10.50		4	3.25
5	11.00		5	3.00

Exploring Marginal Productivity

7. There are two ways of solving the profit-maximizing problem for a firm using the idea that we want to expand an activity as long as the marginal benefit exceeds the marginal cost. We can ask what amount of inputs it should use, and get output from that, or we can ask how much output it should produce, and get inputs from that. The two methods yield the same result and can be illustrated with a very simple example.

Suppose that a firm has only one input, labor, and produces widgets. The production it gets is shown in the table below. The firm can sell output for $2.00, and it can hire labor for $10 per unit of labor. Complete the table below and explain how much labor is should hire how much output it should produce.

Marginal Cost of Labor	Marginal Benefit of Labor	Amount of Labor	Output	Marginal Product	Marginal Benefit of Output	Marginal Cost of Output
		0	0
$10	($20)			(10)	$2	($1)
		1	10
$10	20			10	$2	1
		2	20
$10	16			8	$2	1.25
		3	28
$10	12			6	$2	1,67
		4	34
$10	8			4	$2	2.50
		5	38

Hint: The first unit of labor adds ten units of production and each is worth $2, so the benefit to the firm is $20. The first ten units of output cost $10 to produce, so each producing each adds about $1 to the cost of the firm. That is where the numbers in parenthesis come from. Now finish it.)

8, Welcome to Potter Island where you will learn the economics of pay and productivity. At one time on Potter Island everyone worked for himself. There were only eight workers on the island, and four could produce one pot a day, and four could produce two pots a day. A pot was worth ten cents. What would the people earn?

Then one day an entrepreneur opened a factory. Old skills no longer mattered. The factory had what economists call a production function that looked like this:

Number of Workers	Pots	Marginal Product	Value of Marginal Product
0	0
1 (first)	20	20	2.00
2 (second)	50	30	3.00
3 (third)	70	20	2.00
4 (fourth)	86	16	1.60
5 (fifth)	96	10	1.00
6 (sixth)	102	6	.60
7 (seventh)	105	3	.30
8 (eighth)	108	3	.30

Pots still sell for ten cents. How much will the wage be?

A bit more than .20. That is all that is needed to get everyone to stop making pots individually and go to work for the factory.

(Hint: compute marginal product and the value of the marginal product --which is exactly what it the name says. There are eight workers--how much does that last worker add? Can the employer pay more?)

Suppose that because this first factory is so successful, a second one opens with exactly the same production function. What will happen to wages? (Hint: at what wage will it be unprofitable for either factory to hire away a worker from the other factory? Remember, there are only eight workers total.)

A bit more than $1.00. If the wage was under a dollar, each factory would want to hire five, so the wage would be bid up. Once it reaches $1.00, there is not tendency to bid up wages. This assumes that the two factories do not collude.

Economists say the reason wages are so much higher in the United States than in Mexico is that the environment is more productive for labor in the United States. The most important reason for this higher productivity is that there is more capital per worker in the U.S. How does this example illustrate this idea?

The working environment is better because there is more capital and hence better options for the last worker.

What should happen to wages in Mexico as the amount of capital continues to increase? Suppose the amount of capital does not increase. What will be the likely result for wages be?

If capital increases, the environment for labor should become more productive and wages should increase. If the amount of capital stagnates and the number of workers increases, wages should fall.

Suppose the value of a pot rises to 15 cents. What happens to wages?

Wages should rise up to $1.50. Below that price, both factories would want to hire five workers, so wages would be bid up.

Suppose that after working a year, the workers learn how to work the equipment more productively. The production functions for the two factories now look like this:

Number of Workers	Pots	Marginal Product	Value of Marginal Product
0	0
1 (first)	25	25	2.50
2 (second)	60	35	3.50
3 (third)	85	25	2.50
4 (fourth)	105	20	2.00
5 (fifth)	120	15	1.50
6 (sixth)	132	12	1.20
7 (seventh)	139	7	.70
8 (eighth)	145	6	.60

What will the new wages be?

1.50. Below that the factories will bid up the wage to get more labor.

Economists call the source of this increased productivity "human capital." In this case, labor became more productive by learning on the job. What other ways can people acquire human capital?

Education of various sorts, on the job training.

What you earn is partly a matter of choice and partly a matter of chance (or things you have no control over). What do you control and what is outside your control?

You control effort and to some extent your skills. You can choose to get more education of on-the-job training. You do not control the environment (what other resources are available, which largely determine your productivity), the demand for the product you produce, and to some extent your skills (which can be the result of good genes or a good developmental environment.)