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 abar, lbar and fbar. (Notice that parameters are denoted with an overbar, a convention we will maintain throughout the book.)
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 abar? 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.
(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 (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 lbar increases, what happens to the equilibrium wage and employment levels? Does this make sense? (Hint: think about what happens in the supplyanddemand 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 lbar shifts out the Labor Supply curve Equilibrium wages decrease and equilibrium labor increases. Again, lbar 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 lbar 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 fbar. (1) Solving this graphically. Equilibrium wages increase, and equilibrium employment increases. Again, fbar 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 fbar increases:

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