Suppose that individuals have the following utility function on consumption c and labor h: u(c, h) = c h2 2 A) Assume that there is no tax and that individuals have no other income but their labor income. Solve for the labor supply h as a function of w that maximizes the utility of the individual. B) The government imposes a linear tax on labor income at rate 0 < < 1. Show graphically in a consumption-leisure diagram how introducing the linear tax on labor income modies the budget constraint of the individual. Solve for the labor supply h as a function of w and that maximizes the utility of the individual. What is the effect of increasing on h? C) Suppose that in addition to the linear tax, the government is transferring a fixed amount R > 0 to every individual. That amount R is independent of labor supply choices. Show graphically how the budget constraint is affected by the introduction of R. Solve for the labor supply h as a function of w, , and R that maximizes the utility of the individual. What is the effect of increasing R on h? D) Assume that R = 0 and > 0 as in b). Compute income taxes collected by the government per individual as a function of and w. Draw a graph of taxes collected as a function of . What is the tax rate maximizing tax revenue? E) Suppose that the government has set the tax rate larger than (defined in d)). Can we conclude, no matter what the redistributive tastes of the government are, that it is desirable to decrease ? Make sure to explain your answer.