# ECO101H1 Chapter Notes - Chapter 11: Defined Contribution Plan, Procyclical And Countercyclical, Marginal Revenue Productivity Theory Of Wages

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CHAPTER 11

11-1. Suppose the firm’s labor demand curve is given by:

w = 20 - 0.01 E,

where w is the hourly wage and E is the level of employment. Suppose also that the union’s utility

function is given by

U = w × E.

It is easy to show that the marginal utility of the wage for the union is E and the marginal utility of

employment is w. What wage would a monopoly union demand? How many workers will be

employed under the union contract?

Utility maximization requires the absolute value of the slope of the indifference curve equal the absolute

value of the slope of the labor demand curve. For the indifference curve, we have that

E

w

MU

MU

w

E=.

The absolute value of the slope of the labor demand function is 0.01. Thus, utility maximization requires

that

01.=

E

w.

Substituting for E with the labor demand function, the wage that maximizes utility must solve

01.0

100000,2 =

−w

w,

which implies that the union sets a wage of $10, at which price the firm hires 1,000 workers.

11-2. Suppose the union in problem 1 has a different utility function. In particular, its utility

function is given by:

U = (w - w*) × E

where w* is the competitive wage. The marginal utility of a wage increase is still E, but the marginal

utility of employment is now w – w*. Suppose the competitive wage is $10 per hour. What wage

would a monopoly union demand? How many workers will be employed under the union contract?

Contrast your answers to those in problem 1. Can you explain why they are different?

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Again equate the absolute value of the slope of the indifference curve to the absolute value of the slope of

the labor demand curve:

01.0

*

=

−

=E

ww

MU

MU

w

E.

Setting w* = $10 and using the labor demand equation yields:

01.0

100000,2

10 =

−

−

w

w.

Thus, the union demands a wage of $15, at which price the firm hires 500 workers.

In problem 1, the union maximized the total wage bill. In problem 2 the utility function depends on the

difference between the union wage and the competitive wage. That is, the union maximizes its rent. Since

the alternative employment pays $10, the union is willing to suffer a cut in employment in order to obtain

a greater rent.

11-3. Using the model of monopoly unionism, present examples of economic or political activities

that the union can pursue to manipulate the firm’s elasticity of labor demand. Relate your

examples to Marshall’s rules of derived demand.

Marshall’s rules state that the elasticity of labor demand is lower the

1. lower is the elasticity of substitution;

2. lower is the elasticity of demand for the output;

3. lower is labor’s share of total costs; and

4. lower is the supply elasticity of other factors of production.

Consider two examples: innovations and picket lines. Unions are notoriously bad at allowing firms to

introduce (labor saving) innovations in their factories. The long shoremen on the west coast recently

struck, because they were unwilling to let cargo crates be identified with bar codes. (The union wanted a

union worker to record all movements of crates with pencil and paper.) Thus, the union was pursuing a

policy of limiting the supply of other factors of production (rule 4). In a similar vein, when on strike,

unions picket the firm in order to decrease the ability of the firm to hire scabs (rule 1).

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11-4. Suppose the union only cares about the wage and not about the level of employment. Derive

the contract curve and discuss the implications of this contract curve.

The utility function U = U(w) implies that the union’s indifference curves are horizontal lines, so that the

contract curve coincides exactly with the firm’s labor demand curve (D).

11-5. A bank has $5 million in capital that it can invest at a 5 percent annual interest rate. A group

of 50 workers comes to the bank wishing to borrow the $5 million. Each worker in the group has an

outside job available to him or her paying $50,000 per year. If the group of workers borrows the $5

million from the bank, however, they can set up a business (in place of working their outside jobs)

that returns $3 million in addition to maintaining the original investment.

(a) If the bank has all of the bargaining power (that is, the bank can make a take-it or leave-it

offer), what annual interest rate will be associated with the repayment of the loan? What will be

each worker’s income for the year?

If the bank has all of the bargaining power, it will pay each worker exactly their reservation wage, i.e.,

$25,000. The total cost of this is $2.5 million. Thus, the firm will claim the remaining $500,000 by

imposing a 10 percent interest rate as $500,000 is 10 percent of the original $5 million.

(b) If the workers have all of the bargaining power (that is, the workers can make a take-it or leave-

it offer), what annual interest rate will be associated with the repayment of the loan? What will be

each worker’s income for the year?

If the workers have all of the bargaining power, they will pay the bank its reservation value, i.e., an

interest rate of 5 percent. When it does this, the 50 workers receive $3 million less the 5 percent interest

of $250,000 for a total of $2.75 million. Split evenly among the 50 workers, this leaves each worker with

a yearly income of $55,000.

Dollars

Employment

U

π

D

## Document Summary

Suppose the firm"s labor demand curve is given by: w = 20 - 0. 01 e, where w is the hourly wage and e is the level of employment. Suppose also that the union"s utility function is given by. Utility maximization requires the absolute value of the slope of the indifference curve equal the absolute value of the slope of the labor demand curve. The absolute value of the slope of the labor demand function is 0. 01. Substituting for e with the labor demand function, the wage that maximizes utility must solve w. 100 w which implies that the union sets a wage of , at which price the firm hires 1,000 workers. Suppose the union in problem 1 has a different utility function. In particular, its utility function is given by: U = (w - w*) e where w* is the competitive wage.