Problem 1: Lola from La Jolla consumes housing (H) and food (F). Her student stipend is$600/month.She has a utility function of U(H, F)=FH2 where MUH =2FHand MUF = H2.The current prices are $1 per unit offood and $10 per unit of housing.
(a) Prove that she will consume 40 units of housing and 200 units of food.
(b) The government is worried that her 40 units of housing isn't enough.They agree to subsidize her housing by 50%, lowering the price sheactually pays for housing to $5.If the price of food is $1 and theprice of housing is $5, calculate Lola's optimal bundle of goods.
(c) How much does The Government spend on this program?(c) Calculate her utility level using the utility function above and the quantities consumed with the subsidy.
(d) Calculate Lola's utility maximizing bundle and her resulting utilitylevel if the government chooses to simply give her the money theywould have spent on the program (rather than subsidize housing).Given the two programs cost the same, which one is better for Lola?