Econ 371
Problem Set 4

1. We looked at a number of explanations for the decline in private-sector unionism in class--see your notes.  As for public-sector union growth, one explanation recognizes that labor unions tend to thrive in markets in which labor demand is relatively inelastic. Public sector (i.e., government) jobs are somewhat insulated from competitive pressures on the product market side. Governments don’t have to worry too much about cost constraints since they can simply pass on higher wage costs to taxpayers. Consequently, public sector labor unions do not have to fear employment loss when demanding higher wages.

2. This is in your textbook.

3. Can you distinguish between cause and effect? What is the cause and what is the effect?  We do not know that RTW laws cause unionization to be lower in the sunbelt. It could be that the existing anti-union attitude has created a political environment in which RTW laws can easily be passed.

4.    If unions can be viewed as mini-democracies in which those who are negotiating wages face re-election campaigns, then the leaders will not want to ask for wages so high as to threaten the job of the median voter.  We can interpret the median voter as the union member with the median years of seniority.

5. Impact on the growth of unions:
a) A drop in real wages would tend to increase the demand for unions among workers.
b) An increase in the unemployment rate would tend to decrease the demand for unions.
c) A repeal of right-to-work laws would tend to increase the supply of unions.
d) An increase in earnings inequality would tend to increase the demand for unions.

6.  Worldwide Wickets.  

Labor Output MP MRP Wage Bill
(W=MRP)
Wage Bill
(W=$20)
Group Rent  MR
1 10 10 50 50 20 30 50
2 19 9 45 90 40 50 40
3 27 8 40 120 6- 60 30
4 34 7 35 140 80 60 20
5 40 6 30 150 100 50 10
6 45 5 25 150 120 30 0
7 49 4 20 140 140 0 -10
8 52 3 15 120 160 -40 -20
9 54 2 10 90 180 -90 -30
10 55 1 5 50 200 -150 -40

a)   I've computed the wage bill (= W x L) using the various MRPs as the possible wage rates (since if you plot the MRP versus the number of workers this gives you the labor demand curve off which the firm must make its hiring decisions). In this case, you can see that the wage bill is maximized at L = 6 with W = $25 for a total wage bill of $150. (I know, the wage bill is also $150 for L = 5 and W = $30; by convention, we generally pick the one with the largest L.)  Alternatively, you could calculate where the MR (= Δwage bill/ΔL) = 0.
b)     Total rents is the difference between the wage bill assuming W = MRP and the wage bill assuming W = 20.  I've computed this under the group rent column.  It is maximized at L = 4 and W = 35 with a total of $60 (same caveat applies to L = 3 as above).  Alternatively, you could calculate the MR and find where it crosses the $20 nonunion wage to find the optimal employment level and corresponding wage (which, again, is L = 4 and W = 35).
c)   The firm will not want to hire more than L = 7 given a competitive wage of W = $20; any more hires would entail W > MRP and lower profits.  The firm can not offer anything less than W = 20 because workers can always find jobs elsewhere at that wage.

7.  We did this one for homework.

8.  Strikes may be due to misjudgments or excessive optimism on behalf of either side. Strikes may also be used as a commitment device in order to enhance future bargaining power. Strikes may also be used to shore up membership morale during tough bargaining sessions.

9.  The labor demand curve is taken to be the employment-wage constraint.  A set of indifference curves describes the monopoly union's preferences.  The union will choose the employment-wage combination that maximizes utility subject to the demand curve.  The efficient contracts model suggests that there may be other wage-employment combinations that might be preferable to at least one side of the bargain (while not making the other side worse off).

10.  This is in your notes.

11.  This is in the textbook.

12. Monopoly union model:
a) The optimal wage-employment outcome is where the union's indifference curve is tangent to the labor demand curve. In this case, the slopes of the two lines are equal. The slope of the indifference curve is the ratio of the marginal utility of employment to the marginal utility of the wage, MUE/MUw . Since MUE= w and MUw = E, then the slope of the indifference curve is w/E. This, in turn, must be equal to the slope of the demand curve, namely: w/E = .01. Now, rewriting the labor demand curve as (20 - w)/.01 = E, you can substitute into the demand equation for E from the previous equation and solve for w to get w = 10.
b) To get the employment, plug w = 10 into the demand equation and solve for E = 1000.

13. (a) if the union is willing to drop its demands fast, the firm will find it profitable to delay agreement. A strike, therefore, is more likely to occur. If $5 is the minimum wage that the union is willing to accept, the strike would probably last only 2 months; (b) if the union is willing to accept even lower wages in the future, some firms will find it optimal to wait the union out, so that strikes will be more likely and will last longer; (c) the firm might view the initial wage demand as exorbitant, making a strike almost unavoidable. The strike might not be very long because the union is willing to drop its demands almost immediately after the strike begins.

14. Chilling effect refers to the situation in which arbitration discourages good faith bargaining. The narcotic effect refers to when bargainers are lulled into always using an arbitrator.  Note:  You are not responsible for this topic since we didn't cover it in class, nor is it covered in the textbook.

15.  This is in your notes.

16.  It has been argued that women might rationally choose occupations that require less human capital and provide more flexible work schedules so that they may be able to devote more time to raising a family.

17.  According to Becker's taste for discrimination model, prejudiced employers are willing to pay white workers more than equally productive black workers.  Thus, discriminators will be at a cost disadvantage in the long run.

18.  We did this one for homework.

19.  This would be a great bonus question on the exam.

20. Not necessarily. Salary differentials across academic departments may reflect differing market opportunities for the professors. For example, professors in petroleum engineering are likely to be paid substantially more due to their non-academic job opportunities. It could be that the School of Social Work has very limited non-academic opportunities thereby leading to lower wages compared to the average professor at the school.

21.  This is a great question for the final exam.

22.  This is in your textbook.

23.  This is for you to ponder.