Question 3. A consumer has a locally nonsatiating preference represented by a utility function u(x, y). Assume that u is continuous at all (x, y) where x 2 0 and y 2 0. This consumer's expenditure function is given by Pi 1 2(PiPzu) - P2 if > P2 и E(p1,P2, u) = 1 Pi if P2 и Find this consumer's utility function u(x, y) and the missing formula for E(pı, p2, u). VI
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- 10) Suppose that the utility function of an individual can be described as U(X,Y) = 4X +2Y. For this utility function the MRSA) is always X*YB) is always constantC) is always X/YD) is always X+YE) is always X-Y.ASAP 1. Consider a consumer with utility u(x1,x2) = .5lnx1 + .5lnx2 (b) Now, consider an equivalent representation of the above utility functionx51 x52 Does this utility function have the "increasing difference property"? Howabout the "strict increasing difference" property?Consider the following utility function belonging to “Consumer A”. UA(x,y,z,v) = x0.1y0.2z0.3v0.4. Suppose that prices of x, y, z and v are 1$, 2$, 3$ and 4$. The consumer’s income is 10$. a. Find the values of x, y,z and v that maximize the consumer’s utility subject to his/her budget constraint. b. Suppose that “Consumer B” has a utility function which is a logarithmic transformation of the consumer A’s utility function, i.e. UB =ln UA. Suppose that prices and income are the same. Would the amounts of x, y, z and v consumed by “Consumer B” be the same as the amounts consumed by “Consumer A”?
- Devon's utility function can be written as ?1^0.50?2^0.50, where ?1 is the quantity of hamburgers consumed and x2 is the quantity of milk shakes. His income is $2,400.00. 1) Hamburgers cost $8.00 each and the price of one milk shake is $4.00. If he is maximizing his utility, how much will Devon spend on hamburgers? $ 2)The price of hamburgers decreases to $7.37 each. Now, how much will Devon spend on hamburgers if he is maximizing his utility? $1. Prove if the indirect utility function is quasiconvex The indirect utility function: V(p,w) = w[P1^(p/p-1) + P2^(p/p-1)]^((1-p)/p)When utility function U(q1, q2)=min{ 25.6 q1, 12.5 q2} and q1= 99 and q2= 198 are given, find utility level consumer gains?
- Assume, as in Exercise 22.1, that a consumer has utility function F or fruit and chocolate. Determine the consumer's demand functions q1(P1, P2, M) and q2(P1, P2, M). Determine also It* in terms of P1, P2 and M. Find the indirect utility function and show that It* = 8Vj8M. Suppose, as before, that fruit costs $1 per unit and chocolate $2 per unit. If the income is raised from $36 to $36.5, determine the precise value of the resulting change in the indirect utility function. Show that this is approximately equal to (O.5)λ*, where λ* is evaluated at P1 = 1,P2 = 2 and M = 36. Exercise 22.1 A consumer purchases quantities of two commodities, fruit and chocolate, each month. The consumer's utility function is For a bundle (X1, X2) of X1 units of fruit and X2 units of chocolate. The consumer has a total of $49 to spend on fruit and chocolate each month. Fruit cost $1 per unit and chocolate costs $2 per unit. How many units of each should the consumer buy…J 4 True or false? Be sure to explain your answer in detail. Suppose the utility function u(x1, x2) = 2x1x2 represents a consumer's preferences. Then the utility function v(x1,x2) = x1x2 also represents the same consumer's preferencesAnswer the question on the basis of the following two schedules, which show the amounts of additional satisfaction (marginal utility) that a consumer would get from successive quantities of products G and H. Units of G MUG Units of H MUH 1 36 1 70 2 33 2 60 3 27 3 55 4 21 4 45 5 18 5 30 6 12 6 25 7 6 7 15 If the consumer has a budget of $29 and the prices of G and H are $3 and $5, respectively, the consumer will maximize their utility by purchasing Multiple Choice 3 units of G and 4 units of H. 4 units of G and 2 units of H. 1 units of G and 5 units of H. 2 units of G and 5 units of H.
- Consider the following indirect utility function: v(p, w) = w2 /4p1p2 How can we recover the direct utility function (u(x))?a. Suppose Fiona’s income is $100 per week, which she allocates between chocolates and books. Chocolates cost $2 each. Books cost $10 each if she purchases between 1 and 5 books. If she purchases more than 5 books in a week, the price falls to $5 for the 6th book and all subsequent books. Draw the budget constraint. Is it possible that Fiona might have more than one utility-maximizing solution? b. Confirm that if a consumer’s utility function is described by U = 2X + Y, and prices are px = 2 and py = 1, there is no unique utility maximizing solution regardless of income level. What does this tell you about X and Y as commodities? (Hint: draw a graph showing a budget constraint and indifference curve using the information provided.)10. Consider the utility function U(x, y) = xy + x. Which of the following bundles is noton the same indifference curves as the others. Note: The first entry is the amount of x, thesecond is the amount of y.(a) (5,1)(b) (2,4)(c) (4,2)(d) (2.5,3)