A consumer buys (x1, X2 , X3 ) at price vector (P,, P2 , P3). We make three observations of his behavior:At (P,P,,P;) = (1,1,2), the consumer chooses (x,,x,,x3) = (5,19,9)At (P, P,,P,) = (1,1,1), the consumer chooses (x,,x,, x3 ) = (12,12,12)At (P, P,,P,) = (1, 2,1) , the consumer chooses (x,,x,,x; ) = (27,11,1)%3D%3DDoes the consumer's behavior satisfy WARP? What about SARP?

Recall that, A is revealed preferred to B if A is chosen when B is available. Choices satisfy…

Answered: A consumer buys (x1, X2, X3) at price…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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There are two shows on Netflix that Jeff can watch, Show 1 and Show 2. x₁ measures the number of episodes watched of Show 1 and x₂ measures the number of episodes watched of Show 2. Jeff's preferences can be represented by u(x₁, x₂) = x² + ax². Jeff has 11 hours available for watching Netflix today. Each episode of Show 1 lasts 30 minutes, while each episode of Show 2 lasts one hour. For all question parts, round to three decimal places if necessary. For parts (a) - (f), let a = 1. Draw Jeff's indifference curves for the utility levels u = 4, 9, 16. Draw a straight line between the bundles (x₁, x₂) = (4, 0) and (x₁, x2) = (0, 4). Now, use your picture to determine whether the following two statements are true or false. Answer "1" for true. Answer "0" for false. a) Statement 1: Jeff's preferences are strongly monotone. 1 b) Statement 2: Jeff's preferences are strictly convex. 0 c) Find the bundle at which one of Jeff's indifference curves is tangent to the budget line. (x₁, x^2) = ( d)…
A young consumer has to decide how to spend his spare time. He can either watch movies x or play online video games y. Each round of the game cost 20 and each movie cost 20. He has 200 dollars to spend each week. In addition, he has time constraint. He can spend no more than 20 hours for entertainment each week. A movie last 2 hours and playing a game takes about 1 hour. His utility is given by √xy. Use the Kuhn-Tucker condition to find his optimal choice. (Assume that x and y can take any value, not necessarily integers.) Does the solution satisfy the necessary and sufficient condition for a maximum?
Given the utility function 1/2 1/2 U = x₁x₂find a general expression for MRCS in terms of x₁ and x₂.
A person with utility function U(x, y) = 5 + y + 2x has nonconvex preferences. True False
Suppose you find that MU1(X1Xx2)=2x2 and MU₂(x1+x₂)=2x1. What is the rate at which the consumer is willing to trade good 2 for good 1 at bundle (2,4)? (Note: enter a positive number, i.e. enter the quantity of good 2 that the consumer is willing to give up for an additional-marginal-unit of good 1.) Question 20 Suppose you find that the expressions of the marginal utilities for a consumer are given by MU1 (1,2)= 2 and MU₂ (1,2)= 7. Then you can conclude that: This consumer has Cobb-Douglas tastes For this consumer good 1 and good 2 are perfect complements For this consumer good 1 and good 2 are perfect substitutes None of the above Question 21 Suppose a consumer is always willing to give up 5 units of good 2 for an additional unit of good 1. For this consumer: Good 1 and good 2 are perfect complements Good 1 and good 2 are perfect substitutes Good 1 and good 2 are both essential goods None of the above
A consumer has preferences over two goods, carrots and turnips, each measured in kilograms. For each of the following scenarios, identify which, if any, of the standard assumptions of preferences are violated. (a) The consumer will never eat more than ten kilograms of carrots per day. (b) The consumer cares only about the total weight of the two vegetables consumed, and always prefers more to less. (c) The consumer cares only about the product of the respective weights of the two vegetables consumed, and always prefers a greater product to a lesser one.
A consumer is observed making two choices. First, he faces prices p = (1,3) with wealth w = 8 but is limited to purchasing no more than 3 units of good 1. Given this budget set, he chooses the bundle x = (2, 2). Second, he faces prices p' = (2,1) and wealth w' = 8 with no limit on his purchases of either good. Given this budget set, he chooses the bundle 2' = (4,0). dentify all revealed preferences given these choices. Do this consumer's choices satisfy the Weak Axiom of Revealed Preference? - Could these choices result from the consumer choosing optimally given some mono- tone, convex, and continuous preferences? Explain your answer carefully; you do not have to provide a formal proof.

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