We are given a utility function in which a household lives for just one period. hl+1/e u(c, h) = c – - 1+1/e where we have picked a utility function where hours worked h enter negatively into the...

Extracted text: We are given a utility function in which a household lives for just one period. hl+1/e u(c, h) = c – - 1+1/e where we have picked a utility function where hours worked h enter negatively into the utility function (rather than leisure entering positively). The worker earns a real wage w = . But labor income is taxed at rate T, so that in the budget constraint, the labor income is (1-T)wh. The household doesn't have any assets, so c = wh. Write out the household's optimization problem – utility function and budget constraint. . Solve for the household's optimal labor supply h* and consumption How does the tax rate affect labor supply?