Question

Calculations on Elasticity of Supply and Demand

1. Consider two cities, Control City and Freeburg, that are initially identical, with an equilibrium wage $100, equilibrium employment 100,000 jobs, and 50 million square feet of housing (500 square feet per worker). The government in Control City fixes the maximum total square footage in the city at its current level: new housing can be built, but every square foot of new housing requires that one square foot of old housing be retired from the market. Each city experience an increase in labor demand that shift the market demand curve to the right by 24 percent. In both cities, the wage elasticity of demand for labor is -1.0.

(a) In Freeburg, the wage elasticity of labor supply is 5.0. Illustrate the market effect of the increase in labor demand, including a value for the new equilibrium wage.

(b) In Control City, the wage elasticity of labor supply is 0. Illustrate the market effect of the increase in labor demand, including a value for the new equilibrium wage.

Answer 1

In both the cities,

Equilibrium wage rate, (w) = $100

Equilibrium employment (n) = 100,000

This means, deamnd for labour( D_L​​​​​​) = supply for labour (S_L​​​​​​) = 100,000

Each city experiences increase in labour by 24%

Therefore, new D_L​​​​​​= 100,000+24% =124,000

Each city has wage elasticity of demand for labour(e_dL​​​​​​) = - 1.0

Where e_dL=% change in demand for labour ÷ % change in wage rate

Therefore, % change in wage rate = - 24%

(a). In Freeburg, wage elasticity of labor supply (e_sL​​​​​​) =5.0

Where, e_sL=% change in labor supply ÷ % chnage in wage rate

Therefore, 5 = % change in labor supply ÷ (-24%)

% change in labor supply = - 120%

Thus,labor supply in Freeburg decreases by 120% and is 20,000 workers.

From the given formula of wage elasticity of labor supply, we can calculate the new equilibrium wage rate.

e_sL​​​​= (change in labor supply/original labor supply) ÷ (change in wage rate/original wage rate)

5=(80,000/100,000)÷(change in wage rate/100) {taking the absolute values for change}

Change in wage rate = 160

New wage rate = w + change in w = 100+(160) = $260

Below is the graph illustrating the market effect of increase in labor demand.

​​​​​​In Freeburg, due to increase in demand for labour, there is excess demand at the original wage rate, due to which wage rate decreases and thus supply of labour also decreases. Thus, in ordee to maintain equilibrium wage rate rises.

(b). In control city, wage elasticity of labor supply, (e_sL​​​​) =0

This means change in wage rate has no effect on labor supply.

Therefore the new equilibrium wage rate can be determined through e_dL​​​​​= - 1

{taking the absolute value for change}

e_dL= (change in labor demand/original labor demand) ÷ (change in wage rate/original wage rate)

1=(24,000/100,000)÷(change in wage rate/100)

Chnage in wage rate=24

Therefore new equilibrium wage rate=$124

Below is the graph illustrating the market effect of change in labor demand.

With wage elasticity of labor supply being 0,there is no change in labor supply and due to increase in labor demand there is excess demand for labour. So, in order to attain equilibrium, wage rate rises.