Question

2. Abagail has an estimated Cobb-Douglas utility function of U = 982592.75 for food, 91, and housing, 92. The price for food is arbitrarily set at $1 per unit Pi = $1 and the average monthly rent near UCF, P2, is $1.50 per sq ft. Jackie, like the average UCF student spends $800 on food and housing per month. (a) (20 points) Using calculus, solve for Abagail's optimal quantities of housing and food. For 10 bonus points provide the marginal utility of income (4) (b) (8 points) What is Abagail's utility at the optimal bundle?

Answer 1

We are supposed to do only four subparts to a question. For solution to other parts please post as separate question mentioning the parts to be answered.

2) Utility: us qons a Budget constaints Piq,+ P22M Mue MRS = a) At optimal land, Pr -) MRS: MUI MO 0:25 073 MRS - 0.25qi "Y 0.759. 22 =) At optimal : 192 q P2 MRS = 3 2 2 2 -0.25 a 3 Plau q P ving budget constaint YP, q = M we get a = Tu je 2 =39 ne Uslug M= $800 Pi$ 1 P2 = $1.50 q* = 400 sq.ft Marginal utility of income. ='t q* = 200 0.25 (92 0.25 q b) - (0.25 x 125073 -0.42. Abagait's utility will UL200,499) > (200301 (400jans. U- 336.29,

you sq.ft Now = $1.250 optimal bundle wil be. q= 160 4(1.25) 92 = 3800 4(1.50) Optimal bundle: (48, 2) = 1160,400) Utility will be. Ul160, 400) = (160) U = 317.51 Now (40030.9. d) needed will Money oblained wring. = 336.29 M 70.25 4(1125) 1° 20 Y [lis 70.75 -336.29. =) * (sjó2s [.9.15 ON (336.29] [5802 (0.5, 0.25 M'- 844.27 haum will be. = Money needed to offset the Mi-M M-M- 849.27-800 -$49.27.