Chapter 8 -- Workers, Wages and Unemployment

Problem 1. Earnings and Education For recent data on earnings and educational attainment, go to:

Census Bureau

from which the following data is taken:

Education Median income 2000 Median income 2004
Male Female Male Female
Less than 9th grade $14,149 $8,404 na na
9-12; no HS diploma $18,953 $9,995 $ 21,760 $ 13,280
HS diploma $27,666 $15,120 $ 31,183 $ 19,821
Some college, no degree $33,039 $20,181 $ 37,883 $ 25,235
Associate degree $37,953 $23,270 na na
Bachelor's degree $49,178 $30,489 $52,242 35,195
Master's degree $59,376 $40,246 na na
Master's or doctorate degree na na $ 68,239 $46,004
Doctorate degree $71,738 $48,885

Problem 2. Bob's Bicycle Factory

Note: the text definition of the value of the marginal product of labor is not quite exact enough for this problem. The text definition is simply VMPL = Price times MPL. The full definition is that:

VMPL = (Price - non-labor cost per item) X MPL

In this problem, we must note that the non-labor cost per bike is $100, so that the price minus non-labor cost is $30 per bike.

It is straightfoward to construct the following table, noting that

VMPL = $30 x MPL if price = $130

and that:
VMPL = $40 x MPL if price = $140

as in part c of this problem.

Workers Bikes MPL VMPL (P = $130) VMPL (P = $140)
1 10 10 $300 $400
2 18 8 $240 $320
3 24 6 $180 $240
4 28 4 $120 $160
5 30 2 $60 $80
6 31 1 $30 $40

For the case in which productivity increases by 50 percent:
Workers Bikes MPL VMPL (P = $130)
1 15 15 $450
2 27 12 $360
3 36 9 $270
4 42 6 $180
5 45 3 $90
6 46.5 1.5 $45

Note that the VMPL is the price that employers are willing to pay the last worker hired ; since the simple version of the marginal productivity theory of wages does not regard workers as different in skills, there is no reason for the employer to pay any more to any other worker.

Hence the VPML values just calculated represent the labor demand curve .

Problem 3. Lightbulb factory

In the Bright Idea Lightbulb factory, the marginal product of workers is given by the equation

MPL = 30 - N

where N is the number of workers employed. Lightbulbs sell for $2, and since there are no non-labor costs, we can write the value of the marginal product equation as:

VMPL = 60 - 2N

Since the VMPL equation is the firm's demand curve for labor:

Problem 4. Labor as a derived demand: the auto assembly line

The point of the questions in this problem is that the demand for labor depends on the demand for the product being produced. The demand for labor is therefore derived from the demand for the product, and hence

Problem 5. The supply of labor

Note that in the following, supply = supply curve , and the questions can be rephrased "Does this shift the supply curve?"

Problem 6. Skilled and unskilled workers

In this problem, we must derive two VMPL equations, and use them to find wages for skilled and unskilled workers. We use VMPLS to denote the value of the marginal product of skilled workers, and VMPLU to denote the value of the marginal product of unskilled workers; Ns to denote the number of skilled workers, and Nu to denote the number of unskilled workers.
The equations themselves are simply the price of the output times the given MPL equations:

VMPLS = 600 - 3 Ns


VMPLU = 300 - 3 Nu

The specific questions asked in this problem are:

Problem 7. Trade and wages

Key assumptions of the problem:

As with most assumptions in economics, these assumptions are made to construct a first model of the main forces at work. We might well want to modify them -- to call the goods "software" and "autos" to reflect the comparative advantage of the U.S., to allow worker mobility (as we will do later in the problem, or to allow for slow wage adjustment and unemployment, as we will do later on.


The above information is to be used in the following problems:

Problem 8. Frictional, structural or cyclical?

The classification of the types of unemployment described in this problem is simple:

Problem 9. Minimum wage and disequilibrium

Demand and supply of workers are given by the following equations:

DEMAND: Nd = 400 - 2 w

SUPPLY: Ns = 240 + 2 w

Problem 10. Duration of unemployment

The statistics on unemployment below are from the Bureau of Labor Statistics web site , specifically from the latest Employment Situation News Release . Table A-6 in the January 2002 report gives the percentage distribution of the duration of unemployment -- that is, what percentage of the unemployed were unemployed for less than 5 weeks, from 5 to 15 weeks, and for more than 15 weeks. The data for January 2001 -- a very good month, when the recession of 2001 had not yet started -- should be contrasted with the data for January 2002, with the recession underway.

The January 6,2005 report gives data for December 2004 and 2005.
Note that the percentage unemployed less than 5 weeks has been increased, but long run unemployment is relatively more of a problem now than it was during the recession.
Duration Jan.2001 Jan.2002 Dec.2004 Dec.2005
Less than 5 weeks 46.6 36.8 35.7 37.2
5 to 14 weeks 31.8 31.3 28.2 30.2
More than 15 weeks 21.6 29.9 36.1 32.6