Question

In an economy, the supply of labour is given by S = 10 + 200Wn, where S is the quantity supplied of labour (hours of work), and Wn is the after-tax wage rate (net wage). Assume that the before-tax wage rate is fixed at $10.

a) Find the quantity supplied of labour and the total tax revenue at the following tax rates: 15%, 30%, 50%, 70%, and 80%.

b) Calculate the net wage elasticity of labour supply at each of the tax rates. Is the tax revenue positively or negatively related to the net wage elasticity?

c) What does the relationship between the tax rate and the tax revenue resemble? What is the tax rate that generates the highest level of tax revenue?

Answer 1

(a) The quantity supplied of labor and tax revenue at different tax rates are calculated in the tables below. The top table shows the calculated values, where as the bottom table presents the formula view.

(b) From the labor supply function, the net wage elasticity can be calculated as (dS/dWn)(Wn/S) = 200Wn/S. Accordingly, the elasticity numbers are shown in the top table and the formula can be found in the bottom table above. The diagram below shows the relationship of elasticity and tax revenue. They have both positive as well as negative relationship for different ranges as can be observed.

(c) The relationshop between tax rate and tax revenue can be presented below.

As can be observed, tax revenue is maximum at 50% tax rate.