Elasticity of taxable income

The economy contains two individuals. Jack and Jill. Each has a utility of U = C — L2/2, where L is the

number of hours worked. Jack and Jill earn potentially different wage rates wi. The government imposes

a tax rate of t on income. so that the tax bill of individual i is twiLi. ades the revenue it collects-inalk and

gives it hack to Jack and Jill in the form of a lump-stun transfer.
a. Find the labor supply functions for both Jack and Jill. h. Use this answer to find government revenue

and the size of the transfer. c. What is the elasticity of taxable income with respect to the net-of-tax rate?

d. What tax rate maximizes government revenue? e. What tax rate would maximize a utilitarian social

welfare function?

Sample Solution