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Each day Paul, who is in third grade, eats lunch in school

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Each day Paul, who is in third grade, eats lunch in school. He likes only Twinkies (T) and Soda (S), and these provide him a utility of U(7,S)=1/252 a) If Twinkies cost $0.10 each and Soda cost $0.25 per cup, how should Paul spend the S1 his mother gives him in order to maximize his utility? Hint. Max T/28/2 sct 0.107 +0.255 = 1 (write down the appropriate Lagrange equation and solve for T and S) b) Using your findings from (a), Draw Paul's (consumer) equilibrium (i.c., budget line and the indifference curve) on an appropriately scaled diagram and explain the characteristics of this equilibrium. T How would you convince Paul's mother that his son in fact maximized his utility (i.c., that Paul has convex indifference curves) d) Now compute the (Marshallian) demand functions for Twinkies and Soda. (Write down the appropriate constrained maximization problem and show your work) Hint: Max T/28/2 s. P T + P S = 1 e) If the school tries to discourage Twinkie consumption by raising the price to S0.40, what will happen to Paul's Twinkie and Soda consumption. ) Write down the indirect utility and expenditure functions. Hint: substitute the Marshallian demand functions into U(T',S) = TV2l2 to find the indirect utility V-V(Pr, Ps. 1) Then replace I with E and V with U in the indirect utility function and solve for E to find the expenditure function 8) Now suppose that Paul's mother wants to compensate him for the welfare loss that is caused by the price increase. How much compensation in dollar terms) is required to keep him at his initial utility level after the price increase? (Hint: Compute the expenditure required to keep him at his initial utility level with new prices and compare it with Pauls's initial allowance) 9