Zack's preferences can be represented by the utility function1u(x, y) = r + 2J.x +2/y.1. Assume Zack has income m = 27 and faces pricesp= 6 per unit of thefirst good and q = 3 per unit of the second good. Find Zack's optimalbundle.2. Assume Zack has income m = 36 and the price of the second good isq = 4. Find Zack's demand for the first good, x(p).

eferences can be represented by the utility function 1 u(x, y) : x +2/y. = - 2 me Zack has income m = 27 and faces prices p = 6 per unit %3D good and q = 3 per unit of the second good. Find Zack's of lle.

eferences can be represented by the utility function 1 u(x, y) : x +2/y. = - 2 me Zack has income m = 27 and faces prices p = 6 per unit %3D good and q = 3 per unit of the second good. Find Zack's of lle.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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O let ,U= H (2, Xs)- (t,t 2X3) be a whility funstion da total derivative to ferive MRS O let û (a, Xs)x,+22,, be pns Hher utility funtn Doer "û and u Explain describe the same
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Çağla Ökten 1. Each day, Burcu, who is in third grade, eats lunch at school. She likes only Twinkies (t) and soda (s) and these provide her a utility of U(t, s) = √ts a. Find Burcu's demand for t and demand for s. b. If Twinkies cost $0.1 each and soda costs $0.25 per cup, how would Burcu spend the $1 that her mother give her? c. If the school tries to discourage Twinkie consumption by raising the price to $0.40, by how much will Burcu's mother have to increase her lunch allowance to provide her with the same level of utility she received in part a? 2. Ahmet's utility over good x and y is represented by the following utiity function: U(x, y) = x² + y² Let Px, Py and I denote price of good x, good y and Ahmet's income respectively. a. Graph Ahmet's indifference curves. Is MRS increasing or decrasing in x h Now suppose that Dy-$2 Dv-$4 and Abr car IS.
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solutions. Question 1 Calculating MRS for CD Utility Functions (a) If a consumer has a CD utility function 0.4 0.6 U(91,92) = 994926, calculate MRS1,2. (b) If a consumer has a CD utility function Ima kdown1 calculate MRS1,2. (c) If a consumer has an utility function noltan asd Tor sympy ,1-α U(91,92) = 91 92 llib et (.) orde (hing aid tol bholup U(91,92) = a ln(91) + (1 - a) ln(92), diw sonuanos of calculate MRS1,2. Is it the same as the result in the previous part? (Note: Recall that we discussed the concept of ordinal utility in class, which means only the order of utility matters, not its magnitude. In function is a monotone transformation on the CD utility function. Notice that In (qq) = a ln(9₁) + (1 - a) ln(92). This example verifies that a monotone transformation does not change *(S) sidshav the consumer's indifference curves.) wobei/ (d)
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ê Suppie Concumer bes a utility function 4 x, (x,+2=) and facer a M. 'Derive and giet ber dem and for goed 2.
Question 3 A certain household comprises of a couple, Adam (A) and Betty (B). They have lexicographic preferences over two goods G1 and G2 - A wants to consume as much of G1 as possible, before moving on to G2 whereas, for B, it is the opposite, she wants to consume as much of G2 as possible before moving on to G1.¹ Given their varying preferences, they decide to shop separately, after dividing the household income equally. The household income is $8. One difference to the usual setting - there are government restrictions in place so that no individual is allowed to buy more than two units of either good. Hint: Do not use mathematical brute force (like Calculus) to solve this problem. A simple diagram with appropriate budget lines, etc. should suffice. 1) Suppose prices are p= (P₁, P2) = (1,2). Denote the optimal choice of A and B as a= b= (b₁,b₂) respectively. Solve for a and b. (a1, a2) and
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