Question

The following information is to be used for calculations of the unemployment rate: Suppose there are only two major groups, adults and teenagers, with adults divided into men and women.

Teenagers account for 10 percent of the labor force; adults account for 90 percent. Women make up 35 percent of the adult labor force. Suppose also that the unemployment rates for these groups are as follows: Teenagers, 19 percent; men, 7 percent; and women, 6 percent.

1. Calculate the aggregate unemployment rate.

2. Suppose the share of teenagers in the labor force increases from 10 to 15 percent. How would this affect the aggregate unemployment rate?

The following information is to be used for calculations of the unemployment rate: Suppose there are only two major groups, adults and teenagers, with adults divided into men and women.

Teenagers account for 10 percent of the labor force; adults account for 90 percent. Women make up 35 percent of the adult labor force. Suppose also that the unemployment rates for these groups are as follows: Teenagers, 19 percent; men, 7 percent; and women, 6 percent.

1. Calculate the aggregate unemployment rate.

2. Suppose the share of teenagers in the labor force increases from 10 to 15 percent. How would this affect the aggregate unemployment rate?

Answer 1

(a) The aggregate unemployment rate can be calculated by adding the unemployment rates of different groups weighted by their share of the labor force.

Given share to labor force

Teenagers= 10%

Adult workforce= 90%

Further adults divided into males and females.

Females= 35%

Males= 65%

So aggerate unemployment rate

u=(0.1)(0.19)+(0.9)[(0.35)(0.06)+(0.65)(0.07)]

=0.019+(0.19)(0.021+0.0455)

=0.019+0.05985=0.07885

=7.9%

(b) Since labor force of teenagers increase from 10% to 15%. Then aggregate unemployment also changes

u1=(0.15)(0.19)+(0.85)[(0.35)(0.06)+(0.65)(0.07)]

=0.0285+(0.85)(0.021+0.0455)

=0.0285+0.056525= 0.085025

=8.5%