Question

Thor Odinson has really let himself go. He spends all of his income only consuming whole pies of pizza (2) and cases of beer (b), priced at p: = 5 and p = 15, respectively. Suppose Thor's utility function is given by u(2,5) = 36 and his income is I = 300. (8 points total) (a) Solve for Thor's optimal bundle of pizza pies (2) and cases of beer (b). (2 points) (b) Draw Thor's budget constraint, optimal bundle, and indifference curve (on which the optimal bundle lies) all on the same graph. For full credit, you must include at least 3 points on the IC. Be sure to label the axes and relevant intercepts/points on your graph. (2 points) (c) It is projected that the price of cases of beer will be declining in the near future! Graph Thor's individual demand curve for beer Alien p, equals 15, 10, and 5. Be sure to clearly label your graph. (2 points) (d) Suppose that Thor's friend Korg also spends all of his income only consuming whole pies of pizza (+) and cases of beer (b), priced at P. 15 (same prices as the initial setup). Korg's utility function is given by (3,5) = 2+b and his income is I = 60. Solve for Korg's optimal bundle of pizza pies (2) and cases of beer (b). (2 points) 5 and ps

Answer 1

Perices: (P2, P₂) (5, 15) ulz, b) = 22b2 Odinson's utility : Income - 2262 b 300. Budget constraint: P₂ 24 Pb b = I. a) AL MRS P2 optimal level Pb MRS= M02 - MRS = MUI At optimal b = 1 P2 =) Pb b= P₂2. using 13e 2 P₂ 2 = [2² - I 22²b cue get b* = I 2Pb. 2P2 and (P2, P₃)-15, 15) using on I= 300 2 * = 300 30 we get 10 ol + 300 =10 3o been b) 204 41301103 -14 EBL 1 60 pizza

Demand for pizza - za 300 2P₂ using Pa 15 5 30 Z 10 15 15 10 + to is 30 Quantity of Pizzer, Thor's d) Income a 60 Utility : ) Utz, b) = 2+b. At optimal MRSE P MRS= Muz - 1 MUD Since MRS P2 3 1 3 Therefore The will consume (2,6)= (60, ol. lie & b) = (120) Because Marginal utility per dollar of pizze is greater than to that of beer.