1) (30 points) Teresa is considering going on a vacation this summer. For her trip, she needs to allocate her income of $600 into food (F) and housing (H). Her utility function is 1 1 U(F, H) = FEHz, the price of food is $1/unit and the price of housing is $10/unit. a) (8 points) Because she believes that housing is too expensive, she was able to get a deal with SpaceBnB, which agreed to subsidize her housing consumption with a subsidy of $5/unit. Therefore, the price of housing she faces in this sub-question is $5/unit. Compute her optimal consumption bundle with the subsidy. Show your work. b) (4 points) Considering your result from a), how much is the total value of the subsidy SpaceBnB is giving to her? c) (8 points) SpaceBnB decides to change the deal with Teresa and instead of offering a subsidy of $5/unit of housing, it will simply provide the total value of item b) as a lump sum transfer to her. Compute her new optimal consumption bundle. Show your work. d) (10 points) Without using additional math, will Teresa gain a higher utility from the housing subsidy or the lump sum equivalent transfer? You can either answer it with your own words and/or a graph