Question

Suppose Grand Rapids, MI places a tax τ = $24 on chairs. In the market for chairs, the demand elasticity is ηd = −3, and the supply elasticity is ηs = 1. In the labor market for chair makers, the demand elasticity is ηℓd = −1, and the supply elasticity is ηℓs = 5. In the capital market for chair capital, the demand elasticity is ηk d = −2, and the supply elasticity is ηk s = 1.

1. How much of the $24 tax is paid by consumers?

2. How much of the $24 tax is paid by laborers?

3. How much of the $24 tax is paid by owners of capital?

4. How much of the $24 tax is paid by land owners?

Answer 1

1. We take absolute value of ηd = 3
Share of tax paid by consumers = ηs/(ηs+ηd) = 1/(1+3) = 1/4
Tax paid by consumers = (1/4)*24 = $6

2. Laborer is the supplier of labor.
We take absolute value of ηℓd = 1
Share of tax paid by laborers = ηℓd/(ηℓd+ηℓs) = 1/(5+1) = 1/6
Tax paid by laborers = (1/6)*24 = $4

3. We take absolute value of ηkd = 2
Share of tax paid by owners of capital = ηkd/(ηkd+ηks) = 2/(2+1) = 2/3
Tax paid by owners of capital = (2/3)*24 = $16

4. Supply of land is perfectly inelastic. So, entire tax is paid by land owners = $24.