Bl (Endowments, 25 Points) Sarah has preferences over consumption and recreation time. She does not have any money endowments or any endowments of the consumption good, but she can work at an hourly wage of w =2O in order to buy consumption goods at a price ofp 2931 per unit of consumption. Sarah can, therefore, allocate her time endowment of 24 hours per day between labor supply and recreation. C denotes the quantity of consumption and R denotes the hours spent on recreation. Sarah's preferences are represented by the utility function we, 0) = 2mm) + zmo). (a) Suppose Sarah works 6 hours and consumes 120 units of the consumption good. Compute the marginal rate of substitution at this timeconsumption bundle. Interpret the number you have computed. (b) Find Sarah's demand for recreation and consumption. How many hours will she work? (c) How does the demand for recreation change in response to a change in Sarah's wage? What is the substitution effect for this price change? (d) Suppose that Sarah's hourly wage is raised to 25. Compute the new demand and identify the substitution effect, the ordinary income effect, and the endowment income effect. (e) Argue why the (overall) income effect of a wage change on the demand for recreation is always positive here