(Quasilinear Preferences) A consumer'spreferences over two goods are describedby the following utility function:u(x₁,x₂) = x₂ + Inx, wherex, is theamount of good 1, and is the amountof good 2. Her goal is to choose the bestaffordable bundle, and she has $2available. Quantities must be non-negative, but decimals are fine. (a) Findthe optimal bundle ifp₁ = P₂ = 1. (b) Nowfind the optimal bundle ifp₁ = 1 but= 3.P2Uo1. (Queellinear Preferences) A consumer's preferences over two goods are described by the fol-lowing utility function.wfx)=₂+xwhere ay is the amount of good 1, and ag is the amount of good 2. Ter goal is to choosetan best affordable bundle, and she has 82 available. Quantities naust he non negative, butdecimals are fine.(a) Find the optimal handle if p-2-1.Chy Now End the optimal bandle if p; - 1 bus p: – 3.

Utility function is the function that shows the satisfaction level or measure of usefulness of…

(Quasilinear Preferences) A consumer's preferences over two goods are described by the following utility function: u(x₁, x₂) = x₂ + Inx, wherex, is the amount of good 1, and x2 is the amount of good 2. Her goal is to choose the best affordable bundle, and she has $2 available. Quantities must be non- negative, but decimals are fine. (a) Find the optimal bundle if p₁=p₂ = 1. (b) Now find the optimal bundle if p₁ = 1 but = 3. P₂ 1 (Qualli Preces) A cour's poderences or two goods as described by the fol- Irwing utility function. [x)+JX when ay is the amount of grad 1, nod ay is the amount of good 2. Ter goal is to choose tan bat affordable bendle, and she has 82 available. Quantities naut he aca negative, bet (a) Find the optimal handle if p-p-1. (b) Now End the optional bandle if p 1 bus 3.

(Quasilinear Preferences) A consumer's preferences over two goods are described by the following utility function: u(x₁, x₂) = x₂ + Inx, wherex, is the amount of good 1, and x2 is the amount of good 2. Her goal is to choose the best affordable bundle, and she has $2 available. Quantities must be non- negative, but decimals are fine. (a) Find the optimal bundle if p₁=p₂ = 1. (b) Now find the optimal bundle if p₁ = 1 but = 3. P₂ 1 (Qualli Preces) A cour's poderences or two goods as described by the fol- Irwing utility function. [x)+JX when ay is the amount of grad 1, nod ay is the amount of good 2. Ter goal is to choose tan bat affordable bendle, and she has 82 available. Quantities naut he aca negative, bet (a) Find the optimal handle if p-p-1. (b) Now End the optional bandle if p 1 bus 3.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question 7 A consumer has a utility function 100-(x₁-4)4 -(x2-3)4 and a budget constraint of 9x1+3x2 <200. How much of good 2 do they consume?
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2 Indifference curves Suppose an individual who derives utility u(x, y) from consuming a units of good X and y units of good Y. Derive the indifference curve for a level of utility U for each of the following utility functions. Draw them in the graph below for a utility level U = 18. (A) u(x, y) = 2x + 3y (B) u(x, y) = min{3x, y} (C) u(x, y) = xy
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2) Which of the following utility functions represent the same preferences? Explain. a) U (x₁, x₂) = X₁ X₂ b) W (x₁, x₂) = 5lnx₁ +5lnx₂ c) V (x₁, x₂) = x₁¹/3x₂ ¹/3 - 0.8 d) Z(x₁, x₂) = 0.5x₁ + 0.5x₂
A consumer has utility (see image) on ice creams (x) and cakes (y). (a) Are the indifference curves bowed towards the origin? (b) Derive his demand function (as a function of prices px, py and budget I) for ice cream (x). (c)(Looking at the demand function you found in (b), Is ice cream a normal good? Are ice cream and cakes substitutes or complements? Calculate the income elasticity of market demand at the point px = 2, py = 1 and I = 12.
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Rakhi likes to consume only two commodities X and Y, and nothing else. Both the commodities give her positive utilities, thereby giving rise to her preferences being well- behaved and convex. However, she treats commodity X as an inferior good. Suppose Rakhi earns an income of 1000 per month and the ongoing prices of commodities X and Y are 20 and 10, respectively. (a) Show, with the help of a diagram, what will happen to her optimal consumption of commodity X, in each of the following circumstances: Situation A: Price of X falls to 10, while everything else remains the same. Situation B: Her income increases to 2000, while prices remain the same. (b) What can you say about the demand curve for commodity X that Rakhi’s choice behaviour would produce? Elaborate, with the help of diagram.