Consider Jen, a consumer with preferences U(H,F) = F1/3H2/3, where H is the quantity of housing and F is the quantity of food (per month)

Suppose Jen has a stipend of $600/month which she uses to purchase food at a price of $1/unit and housing at a price of $10/unit. a. Compute Jen's utility-maximizing bundle of goods. b. Suppose that Jen's employer subsidizes housing by paying 50% of her total housing costs, thereby effectively lowering the price Jen pays for housing to $5/unit. Compute Jen's new optimal consumption bundle. c. How much does Jen's employer pay in total for this subsidy? How much utility does Jen enjoy with this subsidy (compute her utility at the optimal bundle). d. Suppose that her employer simply gave Jen the dollar cost you found in (c) as a lump sum (instead of subsidizing housing). Will Jen gain a higher utility from the housing subsidy or the lump-sum equivalent transfer?

a. Jen will consume 40 units of housing and 200 units of food.
b. At a price of $5/unit, Jen will increase housing consumption to 80 and consume 200 units of food as before.
c. The cost to her employer is $5 times 80 = $400. Jen's utility is approximately 109 (utils/month).
d. Jen's optimal bundle when I = 1000 is 333 units of food and 67 units of housing (approximate) and a utility of 114 (approximately). Jen is better off from getting the lump-sum transfer.