Suppose Tammy has a utility function U(C,L) = 2+√(C^2 +L^2), where C is con- sumption and L is leisure. Tammy has a total of T hours for work and leisure. The wage rate is w and Tammy has no non-labor income.
(a) Express Tammy’s utility maximizing choice of work hours in terms of w and T.
(b) If wage rate w decreases, would Tammy’s labor supply increase, decrease, or remain unchanged? Explain why.