1) Elaine wants to keep a good balance of soup and Jujyfruit (a delicious fruit flavored candy) in her diet. Her preferences over bundles of soup and Jujyfruit are represented by the quasi-linear utility function U(S,J) = J0.5 + S, where S and J denote the quantities of soup and Jujyfruit, respectively (Assume fractional quantities of each good can be consumed). Let Ps & Pj denote the prices of the goods and Y denote Elaine's monthly income for spending on these goods. For this exercise, treat soup as the x-axis good. a) Find Elaine's Marshallian demand for soup and Jujyfruit. Is soup a normal or an inferior good? Justify your answer using calculus. Also, calculate the derivative of Marshallian demand for Jujyfruit with respect to income and briefly explain what this implies about the relationship between the demand for Jujyfruit and income for Elaine. b) Now, assume P, = $5 and Ps = $10 and Y = $150. Let U denote Elaine's utility when consuming the Marshallian demanded quantities of Jujyfruit and soup given these prices and income. Use your answers from part a to calculate the value of U. c) Imagine that the price of soup increases to P's=$15. What is Elaine's Hicksian (Compensated) demand %3|

1) Elaine wants to keep a good balance of soup and Jujyfruit (a delicious fruit flavored candy) in her diet. Her preferences over bundles of soup and Jujyfruit are represented by the quasi-linear utility function U(S,J) = J0.5 + S, where S and J denote the quantities of soup and Jujyfruit, respectively (Assume fractional quantities of each good can be consumed). Let Ps & Pj denote the prices of the goods and Y denote Elaine's monthly income for spending on these goods. For this exercise, treat soup as the x-axis good. a) Find Elaine's Marshallian demand for soup and Jujyfruit. Is soup a normal or an inferior good? Justify your answer using calculus. Also, calculate the derivative of Marshallian demand for Jujyfruit with respect to income and briefly explain what this implies about the relationship between the demand for Jujyfruit and income for Elaine. b) Now, assume P, = $5 and Ps = $10 and Y = $150. Let U denote Elaine's utility when consuming the Marshallian demanded quantities of Jujyfruit and soup given these prices and income. Use your answers from part a to calculate the value of U. c) Imagine that the price of soup increases to P's=$15. What is Elaine's Hicksian (Compensated) demand %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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Suppose we are able to model the total utility function for the consumption of two goods, good x and good z. The utility function is structured as U(x, z) = 3x2 + z2 - 2xz. The consumer is faced with the prices of goods x and z. The price for each unit of good x and z is $1 each. The consumer has an income $1 (in thousands). How many units of each good should the consumer consume so as to maximize his/her utility?
There two goods, candy and soda, available in arbitrary non-negative quantities (so the consumption set is R2+). A consumer has preferences over consumption bundles that are represented by the following utility function:u(x, y) = −|4 − x| − |4 − y|where x is the quantity of candy (in grams), y is the quantity of soda (inliters), and |.| denotes the absolute value: for any real number r ∈ R, |r| = r if r ≥ 0 −r if r < 0. The consumer has wealth of w > 0 Dirhams. The price of candy is p > 0 Dirhams/gram, and the price of soda is q > 0 Dirhams/liter. (a) Calculate the utility of the following consumption bundles: (4, 4), (4, 5), (5, 4), (4, 3), (3, 4), and α(4, 5) + (1 − α)(3, 4) for α ∈ [0, 1]. (b) In an appropriate diagram, illustrate the consumer’s map of indifference curves.
Rick consumes 2 goods, Chicken McNuggets (M) with Szechuan sauce (S). His utility function is U(M, S) = M2/3S1/3 and his income is m. The price of Chicken McNuggets is p, and the price of Szechuan sauce is 1. d. Use the equation from part (c) and the budget constraint from part (a) to find Rick’s demand for each of the two goods. e. Suppose m=100 and p=1. How much of each good does Rick consume? Draw a graph showing Rick’s budget constraint and indifference curve passing through his chosen consumption bundle. f. Suppose m=100 and p=2. How much of each good does Rick consume? On the same graph from part (e), show Rick’s budget constraint and indifference curve passing through his new chosen consumption bundle.
Suppose that, by law, a person is required to consume a fixed amount of good X, say X0. Assuming X is a normal good, explain how this law reduces utility for both high and low income people.
Ellie spends £20 on Energy drink (E) and Juice (J). Her preferences for these goods can be described by the following utility function: U ( E,J) = 2E + J^2 ( J squared) - J (MUt = 2, MUj = 2J - 1) Suppose that one energy drink costs £1.60 while one carton of Ellie’s favourite Juice costs £4.00. a) Find Ellie’s optimal consumption bundle. Provide both algebraic and graphical solution. Explain your reasoning. b) Discuss how Ellie’s optimal consumption choice would change when her disposable budget changes. c) If the price of energy drinks increases to £2.00 per can, how should the price of Juice change so that Ellie can be as well off as before this change in prices? d) Discuss the implications of the price change from c) on Ellie’s optimal choice. In your discussion, include the analysis of the substitution and income effects as well as Ellie’s demand for Energy drink and/or Juice.
Liwei consumes X₁ and x2 together in fixed proportions. She always consumes 2 units of X₁ for 1 unit x₂. One utility function that describes her preferences is: u(x1, x2) = 2x1 + x2. u(x1, x2) = min{2x1, x₂}. O u(x₁, x₂) = min{x₁/2, x₂}. u(x1, x2) = 2x1 + 4x2. O u(x1, x2) = 2x1x2.
Assume, as in Exercise 22.1, that a consumer has utility function F or fruit and chocolate. Determine the consumer's demand functions q1(P1, P2, M) and q2(P1, P2, M). Determine also It* in terms of P1, P2 and M. Find the indirect utility function and show that It* = 8Vj8M. Suppose, as before, that fruit costs $1 per unit and chocolate $2 per unit. If the income is raised from $36 to $36.5, determine the precise value of the resulting change in the indirect utility function. Show that this is approximately equal to (O.5)λ*, where λ* is evaluated at P1 = 1,P2 = 2 and M = 36. Exercise 22.1 A consumer purchases quantities of two commodities, fruit and chocolate, each month. The consumer's utility function is For a bundle (X1, X2) of X1 units of fruit and X2 units of chocolate. The consumer has a total of $49 to spend on fruit and chocolate each month. Fruit cost $1 per unit and chocolate costs $2 per unit. How many units of each should the consumer buy…
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Andy purchases only two goods, apples (a) and kumquats (k). He has an income of $1,000 and can buy apples at $10 per pound and kumquats at $10 per pounc utility function is U(a, k) = 4a + 3k. What is his marginal utility for apples and his marginal utility for kumquats? Andy's marginal utility for apples (MU) is MU, = and his marginal utility for kumquats (MU) is MU, = (Enter your responses as whole numbers.) What bundle of apples and kumquats should he purchase to maximize his utility? Andy should consume apples and kumquats. (Enter your responses as whole numbers.) React tv MacBook Air 80 DI DD F1 F2 F3 F5 F6 F7 F8 F9 F10 @ #3 $ % & 1 2 4 7 8. 9 Q W E Y { A S F G H. J C V M ption command command option .. .. V B