5. (10 points total) Consider a household who has the following utility function over consumption and leisure 16-h, where h is the hours of labour supplied (and we assume 16 hours is the maximum anyone can work in a day): (c, 16 h) =log(c) +log(16 h) (a) Find the marginal rate of substitution between consumption and leisure for this household. (1 point) MRS = /(16-h). If you use the inverse ratio, the MRS between leisure and consumption, that's ok as long as your answer to (b) is consistent with it: in that case, you'll have to equate the MRS with the relative price of consumption which is 7/w, not the relative price of leisure which is w. (b) The household receives a real wage w per hour of work and real income d from other sources. Write down the budget constraint, and use it to solve for the optimal combination of consumption and hours worked. (4 points) BC: =w"h + d, or equivalently, + w*(16-h) = w"16 + d. Equating the MRS with the slope of the budget line, we get: c =8'w + 0.5"dand h = 8- 0.5"d/w