For the same set of preferences as in question 5 of this problem set, what is the elasticity of Demand for good XA in terms of the price of the other good?
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A: Answer: Given, U (X, Y) = X2Y2 Income (I) = 100 PX= 10 PY= 5 Let us first find the demand function…
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A: price elasticity of demand for good X e = -3 Price of good X increases = 5
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Q: 2 U(x,y) = x + 1- .2
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Q: Suppose the own price elasticity of demand for good X is -2 and the price of good X increases by 5…
A: Qwn price elasticity of demand for good X e = -2 Price of good X increases = 5%
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- Q- Marginal utility can never be negative. True/FalseProblem 3 Consider a CES utility function. 0-1 0-1\0-1 Uf = + a2 (c2t) Derive u; as 0 → 1.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)?
- Suppose a consumer's utility is given by: u (x1, x2) = a/xT + b/x2 Where a= 8, and b = 4 %3D What is the value of MU1 (x1, X2)when x1=9 and x2=8. (Note: The answer may not be a whole number, so round to the nearest hundredth) (Note: The numbers may change between questions, so read carefully)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…What kind of preferences are represented by a utility function of theform u(x1, x2) = √x1 + x2? What about the utility function v(x1, x2) =13x1 + 13x2?
- You are maxiimizing utility when :A)(MU of X)/(P of X) < (MU of Y)/(P of Y). B)(MU of X)/(P of X) > (MU of Y)/(P of Y). C)(MU of X)/(P of X) = (MU of Y)/(P of Y). D)(MU of X)/(P of Y) = (MU of Y)/(P of X).Donald 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.Given the utility function U (x1, x2) = x³x2.7 select all that are true. a) 30% of the budget is spent on good 1. ○b) V (p, I) = 30.370.7 I 10 P1P2 c) If P2 = 2 and I = 60, then $18 is spent on good 21. d) If P1 = 9, P2 = 2, and I = 60 then the consumer enjoys 1.81 utils of utility. e) Half the budget is spent on good 1 and the other half is spent on 2.
- The purpose of consumption is to satisfy and it is assumed that their utility.You have $3,000 to spend on entertainment this year (lucky you!). The price of a day trip (T) is $40 and the price of a pizza and a movie (M) is $20. Suppose that your utility function is U(TM) T1/3M2/3. a. What combination of T and M will you choose? b. Suppose that the price of day trips rises to $50. How will this change your decision?A consumer has utility function U(x1, X2, X3, X4, X5, X6, X7) = min{/x1x2, /X3X4, VX5X6X7} Find the demand function. 3)