The Labor Market


Review Questions

  1. What is the major long-run determinant of total employment?

 

 Labor supply, which depends heavily on working-age population.

 
  2. What is the major long-run determinant of real wage rates?

 

 The marginal product of labor, which depends heavily on production technology and labor supply.
  3. How would a temporary increase in the growth rate of the working-age population affect employment and real wages in the short run?

 

 Raise employment, lower real wages.

 
  4. How does technical progress, including automation, affect employment in the long run?

 

 Little or no effect.

 
  5. How has NAFTA affected total employment?

 

 Little or no effect.
  6. What are the effects of a tax on labor income?

 

 Reduced reward for work, leading to reduced work effort.
  7. How does an increase in tax rates affect tax revenues?

 

 It may either raise or lower revenues.
  8. How is the unemployment rate defined?

 

 Total unemployment as a fraction of the labor force.
  9. Why can unemployment exist? Frictions in the labor market.  The two essential features of the labor market that are necessary for unemployment to exist are heterogeneity of workers and jobs; imperfect information.

 
10. What is the natural rate of unemployment? The rate of unemployment generated by the economy’s normal rates of job separation and job finding.

 
11. What factors affect the natural rate of unemployment? Demographic factors, government policy, and the pace of economic change.

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Answers to Selected Textbook Problems

Mankiw, Macroeconomics, third edition, chapter 3, problems and applications (repeated from the Production and Distribution module)

3.




 This is a fairly sophisticated question, possibly moreso than the author intended, and a good grasp of microeconomics is required to answer it.  To keep things simple, assume that their are only two goods in the economy, wheat and haircuts (the latter of which is actually a service).  Also assume that there are only two types of workers, farmers and barbers.  Finally, assume that all workers (who are also the consumers) have the same preferences about the mix of wheat and haircuts that they consume.  It is most logical to answer the questions in the following order rather than in the order shown in the text.
f.

 Assuming that both wheat and haircuts are normal goods, increased productivity in the wheat sector causes the output of wheat to rise, lowering the relative price of wheat (and therefore raising the relative price of haircuts).
a-b.

 

 The marginal productivity of labor in the wheat sector rises.  If the real wage of farmers were measured only in units of their own output good, their real wage would clearly rise.  But if their real wage is measured in baskets of wheat and haircuts in the proportions that they actually consume, then their real wage could fall if the relative price of wheat declines enough.
c-d.

 

 The marginal productivity of barbers is unchanged.  If their real wage were measured only in units of their own output good, the real wage would remain unchanged.  But if their real wage is measured in baskets of wheat and haircuts in the proportions that they acually consume, then their real wage clearly rises because the relative price of haircuts goes up.
e.

 

 If workers can move freely between the two sectors, then in equilibrium they must earn the same wage in either sector, measured in terms of baskets of wheat and haircuts in the proportions that they actually consume.   If this were not the case, workers would migrate from the sector with the low real wage to the sector with the high real wage.
g. This means that both types of workers benefit equally from the increase in productivity in agriculture.

Additional comments:
i.







 Without more information, we cannot say which way labor will actually move.  If the income elasticity of demand for haircuts is sufficiently high or the price elasticity is sufficiently low (or some combination of the two), the net effect of the technological improvement in agriculture is to increase the quantity of haircuts demanded.  Because the productivity of barbers has not increased, more barbers are needed to produce the additional haircuts (i.e., the demand for barbers increases).  If the income elasticity of demand for haircuts is sufficiently low or the price elasticity is sufficiently high, the quantity of haircuts demanded falls, reducing the number of barbers.  (Note that the weighted average of the income elasticities for the two goods, where each is weighted by the share of the good in total expenditure, must equal 1.0.  Thus, a high income elasticity of demand for haircuts implies a low income elasticity of demand for wheat.)
ii.





 

 Suppose that workers cannot move freely between sectors.  In fact, suppose they cannot move at all.  Then the wages of the two types of workers need not be equal.  By the reasoning in the answers to parts (c) and (d) above, the real wage of barbers, measured in baskets of wheat and haircuts, must increase.  Thus, technological improvement in agriculture clearly maket barbers better off.  But if the income and price elasticities of demand for wheat are both sufficiently low, then the increased output of wheat causes a large drop in the relative price of wheat.  In this case, it is possible for the real wage of farmers, measured in baskets of wheat and haircuts, to drop, meaning that technological progress in agriculture has reduced the demand for farmers and thus their wages.  (Remember that a low income elasticity of demand for wheat means a high income elasticity of demand for haircuts, which was one of the conditions tending to increase the demand for barbers.)

4.
National saving equals private saving plus public (i.e., government) saving.   In a closed economy (which we assume to be the case here) national saving equals domestic investment.

Mankiw, Macroeconomics, third edition, chapter 5, problems and applications

5. a. Labor demand is given by the marginal productivity of labor.  Assuming that all capital is utilized, the marginal product of labor is given by
MPL = (2/3)(K/L)1/3 = (2/3)(10)L-1/3 = 6.67L-1/3
b. If the real wage can adjust to clear the labor market, all 1000 workers are employed.  Substituting L = 1000 into the MPL equation gives w = MPL = 6.67, and substituting into the production function gives output of 1000.  Aggregate labor income is given by wL = 667.
c. The real wage of 1 is higher than the market-clearing wage.
d. Labor will be hired up to the point where  w = MPL = 6.67L-1/3. 
Solving gives L = 296, output of 444, and aggregate labor income of 296.
e. No.