Question

4- Bart's utility of consuming firecrackers (X) and everything else (Y) can be shown as U(X,Y) = 2 X +Y His marginal rate of substitution can be shown as? MRS = 1/ JE Y is a composite good of everything-but-not-firecracker that Bart buys with $1. His daily income is $20, and the price of firecracker is 50 cents. a. *How many firecrackers will he buy? Use an X-Y graph and sketch the budget constraint and the indifference curve passing through his optimal choice. 1 They can be derived by taking partial derivatives, but we take it as a fact. 2 It can be derived by calculating Mux/m1 but we take it as a fact b. Does U(X,Y) exhibit quasilinear preferences. C. Suppose Homer does not allow him to buy firecrackers. How much would be Bart willing to offer him, so he would allow buying firecrackers? d. Suppose Homer is not around, but Marge plans to offer Bart some money to stop him from buying firecrackers. How much should Marge offer him? e. Consider Bart's demand curve for firecrackers, both Marshallian demand (the usual one) and Hicksian demand (the compensated one). Which one would be steeper?

Answer 1

Q) at Eqm Now MRS=) Ź = PxjPy = 05/1. 2 10-58 , * ()2= 4. from B.C. → - «5x+y=20. Y=20.5x4 = 80-2= 18 Ans U= 2 J4 +18 = QX2) +18 = 22 C go. yes, u(x, y) have Quasi Linear Pref. Ans Bo2 utility is Linear un Y, & concave wot x. c.) If x=0, then Y=20, U= 200+20=20 then max willingness to pay is nice in u, when X is bought