Chapter 1 (Intro to Macroeconomics)

Problem 5 – The labor market model (I). Before you start Number 6 you should probably have a look at this problem. Problem Six builds upon it. There is a “worked exercise” solution at the end of chapter 1.

Problem 6 – The mabor market model (II) – Now we add some parameters values to the labor market model:

The parameters in this setup are a-bar, l-bar and f-bar. (Notice that parameters are denoted with an overbar, a convention we will maintain throughout the book.)

1. The parameter l-bar represents the number of hours workers would supply to the market even if the wage were zero; it therefore reflects the inherent amount of time people like to work.
2. The parameter f-bar, on the other hand, reflects the amount of labor the firm would like to hire if the wage were zero. It might be thought of as some inherent capacity of the firm (perhaps because the firm owns a given amount of land and capital that cannot be altered).

First, be able to draw what this model looks like. It’ll look just like figure 1.7 on page 15. But note that the slope of the labor supply curve is given by the parameter  and the slope of the labor demand is just 

(a) What is the economic interpretation of a-bar?

 is the slope of the labor supply curve – this slope describes by how much people will change their labor supply (how they’ll change their hours worked) given a change of wages. That is; how sensitive workers are to changes in the wage offered. This is the elasticity of labor supply to wages.

Remember that labor supply is defined by regular individual workers preferences for working or not workers.

1. Inelastic  Low .  Let’s say that wage labor is super inelastic: meaning wages can change a lot but people won’t change their supply much. This implies a very low .
2. Elastic  High . Let’s say all people need to supply more labor is a small wage change. Wages go up just a little and people are willing to supply a lot more labor. This implies that  is very large, the slope of the labor supply curve is very steep.

(b) What are the endogenous variables in this model? 

Endogenous variables are variables defined by the model. If you solve the model through, you’ll find values for the quantity of labor supplied (), the quantity of labor demanded 
(). Both of these will be equation to each other, we can call them both equilibrium labor supply (.  We’ll also find equilibrium wages ().

(c) Solve for the equilibrium of the labor market. That is, solve for the endogenous variables as a function of the parameters of the model.  

Find equilibrium   wags by setting the labor demand and labor supply equations equal to each other and solve. You’ll get something like;

Now, plug this equation either (or both) the labor supply or labor demand equation to find equilibrium labor supplied/demanded.

Exam time: I suspect you’ll get real numbers and perhaps a different equation. Thus be ready to work through the actual math involved, and be ready to plug in numbers and solve for 

(d) If l-bar increases, what happens to the equilibrium wage and employment levels? Does this make sense? (Hint: think about what happens in the supply-and-demand diagram for the labor market).

Two ways to solve this.

(1) You can use the graphs and show that  shifts the labor supply equation out (show in a graph that this implies ).

(2) Or use the equations you just worked through to show that

(1) Solving this graphically,

Increasing l-bar shifts out the Labor Supply curve

Equilibrium wages decrease and equilibrium labor increases.

Again, l-bar represents the number of hours workers would supply to the market even if the wage were zero.

(2) Using the equations we just worked through with l-bar increases:

I’d imagine a full credit answer would show the answer via the diagram and your equations.

(e) Answer the same questions in (d) for an increase in f-bar.

(1) Solving this graphically.

Equilibrium wages increase, and equilibrium employment increases.

Again, f-bar reflects the amount of labor the firm would like to hire if the wage were zero.

(2) Using the equations we just worked through with f-bar increases: