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.
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	$				$2	$
		2	20
$10	$				$2	$
		3	28
$10	$				$2	$
		4	34
$10	$				$2	$
		5	38
Hint One: 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. Hint Two: You probably should start by filling in the Marginal Product column.
How much labor should the firm hire to maximize profit? ?? 0 1 2 3 4 5 How much output should it produce to maximize profit? ?? 0 10 20 28 34 38

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. Those who can produce two pots will earn ________ per day. Those who can produce one pot will earn ______ per day.

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	Which Worker:	Marginal Product	Value of Marginal Product
0	0	---	---	---
1	20	first	.	.
2	50	second	.	.
3	70	third	.	.
4	86	fourth	.	.
5	96	fifth	.	.
6	102	sixth	.	.
7	105	seventh	.	.
8	108	eighth	.	.

Pots still sell for ten cents. There is no psychic income from working alone or in the factory. How much will the wage be? _________ (Hint: compute marginal product and the value of the marginal product --which is exactly what it the name says. There are eight workers. The employer wants to maximize profit and the workers want to maximize income. How much does the employer have to offer to make the people work for the factory?)

Suppose that because this first factory is so successful, a second one opens with an identical 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.) _______

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? 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 the likely result for wages be assuming population continues to grow?

Suppose the value of a pot rises to 15 cents. What would change in the table above? What happens to wages?

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

Number of Workers	Pots	Which Worker:	Marginal Product	Value of Marginal Product
0	0	---	---	---
1	25	first	.	.
2	60	second	.	.
3	85	third	.	.
4	105	fourth	.	.
5	120	fifth	.	.
6	132	sixth	.	.
7	139	seventh	.	.
8	145	eighth	.	.

Assuming pots sell for ten cents, what will the new wages be? _________

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

What you earn is partly a matter of choice and partly a matter of chance (or things you have no control over). In this example we see hints of natural ability, acquired ability, the work environment, demand for the output, and maybe, if we look very hard, effort. Which of them you control and which are outside your control?  

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