Labor Market Question Example Standard Mode Derived with Minimum Wage

(a) Solving for the equilibrium values, we set labor demand equal to labor supply. And strive to solve for 

Now that we have equilibrium wages, w-star, let’s solve for labor demand and labor supply.

Labor Demand:

Labor Supply

(b) If a increases, how does wage and employment change?

Looking at the graph:

An increase in a

If  shift down. Also: flatter.

As you can see, Employment increases and wages decrease.

The parameter “a” appears in the labor supply equation, reflecting worker’s willingness to increase or decrease their labor supply given changes in wages. An increase in “a” implies workers increased willingness to supply their labor at every wage rate, increasing equilibrium employment and decreasing equilibrium wages (how am I supposed to fit this into two sentences?).

Basically, if people are willing to work more for less (an increase in “a”), they’ll work more () for less ().

(c) Let a=2, l=1 and f=10. Find equilibrium wages and employment. 

(d) Finally, using the parameters from (c) consider a minimum wage: w-bar=5. Under the minimum wage what is the new equilibrium level of employment L-star? Is there an excess of labor supply? How much? 

A binding minimum wage is when the minimum is above the equilibrium wage.

At $5 wages, let’s find labor supply and labor demand.

Labor demand:

Labor Supply:

Although workers are willing to supply 11 units of labor, firms are only willing to purchase 5 units. The new equilibrium employment is 5. That’s 2-units less than no-minimum-wage equilibrium. And 6 units less than workers are willing to supply at a $5 minimum wage (the labor surplus is 6).

A minimum wage in general:

Now, parameterizing the diagram.