Question

Suppose that Labor Supply is given by:

L Supply = 5w

Labor Demand had been such that the equilibrium wage rate was $20; however, a negative shock hit labor demand so that the new Labor Demand is given by:

L Demand = 55 - 0.5w

Suppose that the shock to labor demand affected only the labor demand curve's intercept and not its slope. What must have been the pre-shock intercept for labor demand (ie the quantity of labor demanded if w=0) in order for $20 to be the equilibrium wage?

Answer 1

New labor demand (after shock) is given by:

L_Demand = 55 - 0.5w

Note: -0.5 is the slope of labor demand curve after shock.  

and

55 is the is the after shock intercept for labor demand (i.e., quantity of labor demanded if w=0)

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Pre-shock condition:

Suppose that the shock to labor demand affected only the labor demand curve's intercept and not its slope.

Let's assume X is the pre shock labor demand curve's intercept and slope of pre shock labor demand will be unchanged at -0.5

Pre-shock labor demand curve is given by:

L*_Demand = X - 0.5w

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Labor supply curve is given by :

L_supply = 5w

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Pre- shock equilibrium in labor market occurs at the following point:

L*_Demand = L_supply.

=> X - 0.5w = 5w

The equilibrium wage rate was $20 pre-shock. So put w = 20

=> X - 0.5(20) = 5(20)

=> X - 10 = 100

=> X = 100 + 10

=> X = 110

The value of X is 110.

It means  the pre-shock intercept for labor demand (ie the quantity of labor demanded if w=0) is 110 in order for $20 to be the equilibrium wage.

Answer: 110