Standard Labor Market Model with Taxes

Exam Time –  I should make it clear that you’ll probably not get exactly (or all that close) to this problem. Thus focus on the steps you take toward a solution. Also, review Oct 18 lecture notes.
  1. Equilibrium labor supplied and demanded is the value of  such that .  What we do is set the labor demand curve equal to the labor supply curve, and solve for . You can then plug that into either equation, and it’ll provide the same value of 

And this will also be equal to

This two messy equation, given values for  will be equal!

  1. If taxes, then , which implies that

  1. Starting with wages:

This makes the  term smaller, thus the denominator smaller, making bigger.

Therefore the wage workers insist upon and the wage employers must now pay is higher than without taxes. Note, though, that worker’s take-home wage is , after tax wages.

For how Equilibrium Labor is affected by positive income tax – I’m going to use the equilibrium labor demand equation,  since there is only one  term appearing in it (while the labor supplied equation  has two  terms, which would make the discussion more complicated)

  • This makes the  term smaller, making the denominator smaller in the  term.
  • The smaller denominator makes the  term larger.
  • With the negative sign in front of the bigger term, this makes  smaller.  

Graphically, you also want to show figure 7.4 on page 171.



Labor Demand:

Which should equal Labor Supplied:

And we know that labor supplied equals labor demanded. So you should solve the  that is easiest mathematically. Or both if you really want that 100%



Labor Demand:

Which should equal Labor Supplied: