C. Claire consumes food and clothes. Her utility function is U(f, c) = 2In f + c, where f is the amount of food and c is the quantity of clothes Claire consumes. The prices for food and clothes are py and pe (dollars per unit), respectively. Claire has an income of m (dollars). (1) Find Claire's Marshallian demand functions for food and clothes. (2) Suppose Claire's income m is $400 and py = 10, and Pe = 20. What is Claire's best affordable bundle? Suppose the government decides to subsidize Claire's food purchases in the amount of $5 per unit. What is Claire's best affordable bundle? What is the total amount of subsidy Claire receives from the government? (3) Let T be the total amount of subsidy you calculated in (2). Suppose the government decides to simply pay Claire a lump sum of T dollars instead of the subsidy for food purchases given in (2). What is Claire's best affordable bundle? (4) Which scheme of subsidy does Claire prefer