Suppose Mary has the utility function U(x1, x2) = v(xi) +2x2 with v such that v' > 0and v" < 0. Suppose initially Mary chooses the optimal bundle x = 10 and x2 5.What is the new optimal x if prices for both xj and x2 are cut in half (reduced by50%)?%3DOx1 = 5X1 = 11.7Ox1 = 20O None of the other answers are correctOx1 = 10%3!

Given, Utility Function, U(x1,x2) = v(x1)+ 2X2, v such that v'>0 and V"<0 As mentioned, x1 =…

Suppose Mary has the utility function U(x1, x2) = v(x;) + 2x2 with v such that v' > 0 and v" < 0. Suppose initially Mary chooses the optimal bundle x = 10 and x = 5. What is the new optimal x if prices for both x and x2 are cut in half (reduced by 50%)? Ox1 = 5 Ox1 = 11.7 Ox1 - 20

Suppose Mary has the utility function U(x1, x2) = v(x;) + 2x2 with v such that v' > 0 and v" < 0. Suppose initially Mary chooses the optimal bundle x = 10 and x = 5. What is the new optimal x if prices for both x and x2 are cut in half (reduced by 50%)? Ox1 = 5 Ox1 = 11.7 Ox1 - 20

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Suppose Mary has the utility function U(1, 22) = v(æ1) + 2x2 with v such that v > O and v" < 0. Suppose initially Mary chooses the optimal bundle æ = 10 and x2 = 5. What is the new optimal x1 if prices for both r1 and x2 are cut in half (reduced by 50%)? 1 = 20 X1 = 5 O æ = 10 X1 = 11.7 %3D None of the other answers are correct
Show whether or not the following utility functions are monotonic transformation of each other u = X,X2: u = lnX,lnX, %3! u = X, + X2: u = (X, + X,) u = X, + X2: u = (X1 + X2)? Show whether or not the following utility functions are convex U = x,°X, U = x, + X,2 U = X, + X,X2X
Suppose that a fast-food junkie derives utility from three goods-soft drinks (x), hamburgers (y), and ice cream sundaes (z)− according to the Cobb-Douglas utility function U(x,y,z)=x0.5y0.5(1+z)0.5. Suppose also that the prices for these goods are given by px=1,py=4, and pz=8 and that this consumer's income is given by I=8.a. Show that, for z=0, maximization of utility results in the same optimal choices as in Example 4.1 . Show also that any choice that results in z>0 (even for a fractionalz ) reduces utility from this optimum.b. How do you explain the fact that z=0 is optimal here?c. How high would this individual's income have to be for any z to be purchased?
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Suppose a consumer’s utility function is u = x_1^(3/2) x_2^(3/2) . She spends her budget of £27 for two goods. The prices of both goods are p1 = 6 and p2 = 6 Now suppose that instead both goods are priced as follows: There is a discount of 50% on the price of good 1 on each additional unit in excess of 3 units, and there is a discount of 50% on the price of good 2 on each additional unit in excess of 3 units. Draw the new budget constraint and derive it analytically.
6. Suppose that a fast-food junkie derives utility from three goods - softdrinks (x), 0.5 hamburgers (y), and ice cream sundaes (z) – according to the Cobb-Douglas utility function U(x, y, z)=x5y5 (1+z)05. Suppose also that the prices for these goods are given by p=0.25, p, = 1, and p. = 2 and that this consumer's income is equal to 2. a) How much will this consumer buy of each good to maximize utility? b) Show that the utility function is maximized (Use |H₂| to identify whether it is a maximum or a minimum). c) What is the maximum utility of the fast-food junkie?
Your sister’s utility function over the 2 goods X and Y is defined by: U (X,Y) = XY +4Y a. If she originally consumed 10 units of X and 24 units of Y, and if the consumption of X were increased to 12 units, how much Y would she be willing to give up and maintain the initial level of satisfaction? That is, how much less Y is needed in exchange for the increase in the consumption of X if she is to be equally satisfied before and after the change occurs? b. On a carefully constructed graph (you only need to consider X and Y values up to 50), indicate your sister’s original consumption position, with X plotted on the horizontal axis and Y on the vertical axis. Draw her indifference curve through the original consumption bundle from part a. As you can verify (or have already verified), she is indifferent to the points (10,24) and (12,21). If you double the amount of each good in these two consumption bundles, you would have the bundles (20,48) and (24,42). Since the two original bundles…
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A) Suppose a quasilinear utility function is given by u(x₁, x₂) = 2√√x₁ + 4x₂. 1. For this utility derive the demand functions xi (P₁, P2, 1) and x₂ (P₁, P2, 1). 2. For this utility derive the Engle function I = 1(x₂, P₁, P₂) for good 2. B) Do the same for the Cobb-Douglas utility function u(x₁, x₂) = x₁x². That is, 1. For this utility derive the demand functions x₁ (P₁, P2, 1) and x₂ (P₁, P2, 1). 2. For this utility derive the Engle functions I = 1(x₁1, P₁, P₂) and I = = 1(x₂, P1, P2).
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