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- 2 3) For each utility function, determine the marginal utility with respect to x, marginal utility with respect to y, and the MRS. (3pts each) a) U(x, y)-3x+2y b) U(x, y) 10x¹/5 y c) U(x, y)=x+ y²If the utility function (U) between food (F) and clothing (C) can be represented as U = F*C, then which combination of food and clothing will a rational consumer choose? a. (F, C) = (9, 25) O b. (F, C) = (25, 4) O c. (F, C) = (4, 16) d. (F, C) = (4, 25)Q- Marginal utility can never be negative. True/False
- Suppose that you go to a restaurant with your friends. a) One of your friends always eat exactly one chicken wrap (C) and drinks two cups of ayran (A). He never changes this combination of food choice. (i) Write the utility function of your friend to represent his preferences. (ii) Draw couple of indifference curves of your friend on graph with appropriate labels. (iii) Determine the demand function of your friend for each product as a function of prices and income. Denote prices as Pc, Pa; income as M. b) Suppose that one of your friends does not care if she consumes spaghetti(S or noodle(N).She wants to consume either two-dish spaghetti or two-dish noodle or any combination of both which adds up to two dishes. (i) Write the utility function of your friend to represent his preferences. (ii) Draw couple of indifference curves of your friend on graph with appropriate labels. (iii) Denote prices as Pn, Ps; income as M. If Pn < Ps, then determine the demand…Problem 3 Consider a CES utility function. 0-1 0-1\0-1 Uf = + a2 (c2t) Derive u; as 0 → 1.A5
- Typed Plzzzz And Asap I will upvoteIce 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)?c only please
- 5. Suppose u(x) = max{ar₁, ßr2} for parameters a, ß > 0). (a) Will this consumer will spend all their money (i.e. choose z so that px = m)? Why or why not? (b) Show that either r = 0 or r2 = 0 that is, the consumer buys only one of the two goods. (c) Solve the consumer's problem. What is z? [Hint 1: The first question, and the previous part of this question, might be helpful here. Hint 2: The price ratio might be relevant to the consumer's behavior.]PLEASE SHOW SOLUTIONS AND PLEASE DO THIS TYPEWRITTEN FOR UPVOTEConsider a consumer whose preferences can be represented by the utility function u(x, y) = x + y (a) Originally, px = 1, py = 2 and m = 1. What bundle does the consumer choose, and what is his utility from this bundle? (b) The price of good x then rises to 3. What bundle does the consumer choose after the price change, and what is his utility from this bundle? (c) Calculate the compensating variation. (Hint: at the new price ratio, what good will he spend his income on?) (d) Calculate the equivalent variation.