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- Ice cream and cakes are perfect substitutes for a child, and 2 units of ice cream is always worth 3 units of cakes (however many ice creams or cakes she might have, she would be willing to give up 2 ice creams to get 3 more cakes to keep the same utility level) . (a) Write down a utility function u(x,y) that represents the child's preferences, where x is the number of ice creams and y is the number of cakes she has. (b) If the prices are px= 8 and py =5, and she has $140 to spend on the two goods this summer, what is her optimal bundle? (c) If the price of ice creams decreases slightly, down to px = 7, what happens to her optimal bundle in this case? Did it change "slightly" compared to (b)?For the following utility function find the MRS at (x, y) = (2, 3) a) U(x, y) =2x +y b) U(x, y) =x^3 y^2 c) U(x, y) =min(x, 2y) Solve subparts (c )correctlyCharlie's utility function is (1-a) U(xa, XB) = Ax“xr-) where A > 0 and a > 0
- The goal of the consumer is to maximize the total utility or satisfaction derived from their purchase choices, given the unique budget constraint. To calculate total utility of a given combination of T-shirts and movies, one would use the following approach: Group of answer choices For a given combination of T-shirts and movies, assign a number of utils to that combination. For a given combination of T-shirts and movies, survey a group of individuals to determine an average for utils to be assigned to the number of T-shirts and movies. Use utils as a measure of utility, assigning a specific number to T-shirts and movies, and then add those together. For a given combination of T-shirts and movies, use Google to identify the number of utils associated with the number of T-shirts and movies and then sum them.b) Define indifference curve and discuss the characteristics of an indifferencecurve.Consider a utility function given by:
- Typed Plzzzz And Asap I will upvoteDonald likes fishing (X1) and hanging out in his hammock (X2). His utility function for these two activities is u(x1, x2) = 3X12X24. (A) Calculate MU1, the marginal utility of fishing. (B) Calculate MU2, the marginal utility of hanging out in his hammock. (C) Calculate MRS, the rate at which he is willing to substitute hanging out in his hammock for fishing. (D)Last week, Donald fished 2 hours a day, and hung out in his hammock 4 hours a day. Using your formula for MRS from (c) find his MRS last week. (E) This week, Donald is fishing eight hours a day, and hanging out in his ham mock two hours a day. Calculate his MRS this week. Has his MRS increased or decreased? Explain why? (F) Is Donald happier or sadder this week compared to last week? Explain.Eren’s two main hobbies are taking vacations overseas (V) and eating expensive meals (M). His utility function is given as: U(V,M) = V^2MLast year, the average price of taking a vacation overseas was US$200 and the average price of an expensive meal is $50. However, due to supply problems in Onions, the average price of an expensive meal rose to $75. The average price of a vacation did not change. His income, which is $1500, did not change. Suppose that the Department of Welfare wants to know how much should be given to Eren to offset his change un utility due to the price increase of an expensive meal. Calculate the compensative variation (CV).
- Draw an indifference map for each of the following functions. U(x,y) = x2y3U (x, y) = 2x + 3yU (x, y) =x + ln(y)U (x, y) = min{2x, 3y}U (x, y) = max{3x, 2y}A consumer buys (X1, X2 , x3 ) at price vector (P1, P2 , P3). We make three observations of his behavior: At (P.P,P,)=(1,1, 2), the consumer chooses (x,,x,,x, ) =(5,19,9) At (P.P,,P.) =(1,1,1), the consumer chooses (x,.x,,x, ) = (12,12,12) At (P,P,,P,)= (1,2,1), the consumer chooses (x,.x,,x, ) =(27,11,1) Does the consumer's behavior satisfy WARP? What about SARP?Consider the following utility functions. G(x,y) = x² + 3y² H(x,y) = (x+1)¹/2 + y + 1 L(x,y) = xey U(x,y) = In(x) + y² W(x,y) = 100 x - 4x² + 3 y Z(x,y) = (x)¹/² + y Which function or functions have strictly convex indifference curves (at every point where x>0 and y>0)?
