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

Consider a consumer with the utility function U (x1, x2 ) = 10x12/3x21/3 −50. Suppose the prices of x1 and x2 are 10 and 2 respectively and the consumer has an income of 150. How would the optimal bundle change if the utility function was log- linear: 2lnx1 +lnx2?

What is the demand for goods L and Y given the utility function U(L,Y) = L+2Y where the price of L is $1 dollar per unit and the price of y is $Z per unit.

(2) Lisa can buy either whole chickens or chicken wings at her local supermarket. Her utility function over whole chickens and chicken wings is U(xc,Xw) = 2xc + Xw, where x, and xw are chickens and chicken wings, respectively. What is her demand function xc (pc, Pw, m) for chickens?

Given the utility function, where U is the total utility and x and y are the commodities consumed, find the marginal utility function of each of the two commodities.

Utility over quantities of two goods is given by U(q1, q2) = q1 + In q2. Which of the following statements is always true about the demand functions for good 1 and good 2 if consumer faces prices pi and P2 and has income M? The demand function of good 1 does not depend on M. The demand function of good 2 does not depend on M. The demand level of good 1 is always greater than zero. The demand level for good 2 is always greater than the demand level for good 1. O None of the other statements are true.

Harry spends his weekly income M > 0 on two commodities, food (X) and rental videos (Y). His utility function is U (X,Y)=2-√x+2·√Y The price of food is Px > 0 and the price of rental videos is Py > 0. Is any of the two goods, food or rental videos, an inferior good for Harry? (

Suppose that your tastes over coke(X1) and burgers(X2) can be summarized by the utility function: u(X1, X2) = (X12X2)1/3. (a) Calculate the optimal quantity of coke and burgers' consumption as a function of P1, P2 and I. (b) Illustrate the optimal bundle A when P1 = 2, P2 = 10 and weekly income I = 180. What numerical label does this utility function assign to the indifference curve that contains bundle A? (c) Using your answer, show that both coke and burgers are normal goods when your tastes can be summarized by this utility function. (d) Suppose the price of coke goes up to $4. Illustrate your new optimal bundle and label it, C. (e) How much coke and burgers would you buy if you had received just enough of a raise to keep you just as happy after the increase in the price of coke as you were before(at your optimal income of $180)? Illustrate this as bundle B. (f) How large was your salary increase in the previous part? (g) Now suppose the price of burgers (P2) falls to $5 (and…

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Suppose that Monica has income of $120, and faces prices Px = $2.9 and PY = $2.5, where x = number of cups of Starbuck coffee and Y = number of cups of MacCafe. Her goal is to maximize her utility, described by the function U=2x+ Y. a) Represent graphically the problem Monica faces. Make sure you identify your axes as well as your budget constraint and indifference curves. Also identify the optimal bundle. b) Calculate the optimal bundle. Make sure you show all your calculations.