Question

I only need answer for part D please.

3. Sam and Dean are twin brothers. Each gets a weekly allowance of $2. Sam's preferences for fidget spinners (good and water guns (good y) can be represented by the utility func- tion u(x, y) -xiyi. Suppose that both goods are S1 per unit. (a) Solve for Sam's optimal consumption bundle. (b) Suppose p rises to $2. What is Sam's new optimal consumption point? (c) How much would his parents have to increase his allowance in order to leave him exactly as well off as he was originally? (d) Dean's preferences are represented by v(z,y)-흘 In(z) + 흘 ln(y). Answer parts (a)-(c) for Dean. Comment.

Answer 1

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NOw 8o at Neuo puies, ouginal uhaty shoud be mainteine 2n (M/4) + Dn (/a) -O Thus atu aniwers ate same, buor the puejesence" ale exactu similar fo two (people-

Since preferences of Dean can be written as v ( x,y) = ln ( x^.5*y^.5)

Which is just monotonic transformation of Sam preferences, hence MRS is same, so this all results.