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2) Optimal choice: example #2 Emi's friend Xindi also likes tacos, but she doesn't like sandwiches. Instead, she always consumes exactly two tacos (good x) with one glass of horchata (y), and she doesn't enjoy either good without the other. Suppose prices are the same as initially in problem 1, so that horchata is twice as expensive as tacos (Px=$2, Py=$4), and Xindi has the same budget as Emi: I=$24 a) Propose a utility function that is consistent with these preferences and draw a couple of its isoquants. b) Solve Xindi's long run utility maximization to find the basket of goods she will purchase. c) What if, just as in problem 1, the good on the x axis goes on sale for $1/ unit?

2) Optimal choice: example #2 Emi's friend Xindi also likes tacos, but she doesn't like sandwiches. Instead, she always consumes exactly two tacos (good x) with one glass of horchata (y), and she doesn't enjoy either good without the other. Suppose prices are the same as initially in problem 1, so that horchata is twice as expensive as tacos (Px=$2, Py=$4), and Xindi has the same budget as Emi: I=$24 a) Propose a utility function that is consistent with these preferences and draw a couple of its isoquants. b) Solve Xindi's long run utility maximization to find the basket of goods she will purchase. c) What if, just as in problem 1, the good on the x axis goes on sale for $1/ unit?

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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refer to question 1 but answer question 2 

Consider the utility function U(x,y) = xy, which describes the enjoyment Emi gets from consuming tacos (x) and sandwiches (y) over a period of 1 week. a) Does Emi like both tacos and sandwiches? Does she like variety? b) Let Emi have budget I=$24, and let prices be Px=$2, Py=$4. Find Emi's optimal basket of goods x and y. Is this an interior or a corner solution? c) What will happen if tacos (good x) go on sale for $1? Find the new optimal bundle. 2) Optimal choice: example #2 Emi's friend Xindi also likes tacos, but she doesn't like sandwiches. Instead, she always consumes exactly two tacos (good x) with one glass of horchata (y), and she doesn't enjoy either good without the other. Suppose prices are the same as initially in problem 1, so that horchata is twice as expensive as tacos (Px=$2, Py=$4), and Xindi has the same budget as Emi: I=$24 a) Propose a utility function that is consistent with these preferences and draw a couple of its isoquants. b) Solve Xindi's long run utility maximization to find the basket of goods she will purchase. c) What if, just as in problem 1, the good on the x axis goes on sale for $1/ unit?
Transcribed Image Text:Consider the utility function U(x,y) = xy, which describes the enjoyment Emi gets from consuming tacos (x) and sandwiches (y) over a period of 1 week. a) Does Emi like both tacos and sandwiches? Does she like variety? b) Let Emi have budget I=$24, and let prices be Px=$2, Py=$4. Find Emi's optimal basket of goods x and y. Is this an interior or a corner solution? c) What will happen if tacos (good x) go on sale for $1? Find the new optimal bundle. 2) Optimal choice: example #2 Emi's friend Xindi also likes tacos, but she doesn't like sandwiches. Instead, she always consumes exactly two tacos (good x) with one glass of horchata (y), and she doesn't enjoy either good without the other. Suppose prices are the same as initially in problem 1, so that horchata is twice as expensive as tacos (Px=$2, Py=$4), and Xindi has the same budget as Emi: I=$24 a) Propose a utility function that is consistent with these preferences and draw a couple of its isoquants. b) Solve Xindi's long run utility maximization to find the basket of goods she will purchase. c) What if, just as in problem 1, the good on the x axis goes on sale for $1/ unit?
Expert Solution
Step 1

Preferences of  Xindi : Two tacos(x) with one glass of horchata(y). She does not enjoy either good without the other.

Px=$2 and Py=$4 and I=$24

Goods are complements as they are taken together and any single good provides zero utility.

(a) Her utility function : U=min{x,2y}

As both goods are consumed together (x=2y), when

y=1, x=2

y=2, x=4 and so on.

The isoquants will be L-shaped.

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