Which of the following statement is TRUE based on this question : A utility function with 2 goods (X,Y) is given by U = X^1/2Y. If there’s 3 bundles, bundle A = (9,3); bundle B = (4,1); bundle C = (16, 4

Which of the following statement is TRUE based on this question : A utility function with 2 goods (X,Y) is given by U = X^1/2Y. If there’s 3 bundles, bundle A = (9,3); bundle B = (4,1); bundle C = (16, 4

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Anton, Betsy and Catherine are three college friends who regularly go the movies. At the movies, they can purchase skittles (x) and junior mints (y). The table below display the total utility each of them get from bundles of these two snacks (x, y). Bundle A = (1,1) B = (1,2) C = (1,3) D = (1,4) E = (1,5) Anton's Anton's Utility MUY (2) (1) 10 14 16 17 17.5 Betsy's Utility (3) 10 10 9 8 7 Betsy's MU, (4) Catherine's Utility (5) 10 12 15 19 24 Catherine's MUY (6) a) Yesterday the three friends went to watch the Barbie movie and they purchased the same bundle, bundle B = (1,2), with 1 bag of skittles and 2 bags of junior mints. Can you say who of the three friends experienced the highest utility from consuming bundle B? Explain. b) As you may have noticed, all bundles in the table contain 1 bag of skittles while they differ in the number of bags of junior mints. Fill in columns (2), (4) and (6) in the table by computing the marginal utility each friend receives from choosing a bundle…
Assume that a person’s utility depends on two products, x and y. The utility function is given by U(x, y) = (x + 2)^2(y + 3)^3. Find the marginal utility of x and marginal utility of y.
Suppose that a consumer has the utility function U(X,Y)= 2X 1/2 y 1/2 for X>0 and Y> 0. Which of the following utility functions would not represent the same preferences? U(X,Y)= 2(X + Y) 1/2 U(X,Y)=2x1/2y 1/2 - 100 O U(X,Y)= In 2 + InX+ In Y O U(X,Y)= X 1/2 y 1/2 O U(X, Y) = 4XY
Problem 2.3 Let the consumer's preferences over consumption bundles (x1, x2) be represented by the utility function u(x1,X2) = /x1 +1·(x2+1). Which of the following statements is correct? (a) The utility function v,(x1,x,) = In(x, + 1) + 3 ln(x, + 1) also represents the consumer's preferences. (b) The utility function v,(x1,x2) = In(x1 + 1) + In(x2 + 1)² also represents the consumer's preferences. (c) None of the statements is correct.
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…
A consumer’s utility only depends on the consumption of goods A and B according to the following Cobb-Douglass utility function: U(A, B) = A1/4 B 3/4. The price of goods A and B are $20 and $40, respectively. The consumer has a budget of $1200 that he can use to consume the two goods. a. Write down the budget constraint and plot it. b. Calculate the optimal bundle and maximized utility for the consumer. c. A new tax of $10 is imposed on the price of good B. Compute the new optimal bundle of good A and B for the same consumer. What is the utility loss due to the tax? d. Show that the consumer would prefer a lump sum income tax that raises the same revenue as the tax on good B. Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.
Suppose the utility function of U(x1, x2) = x11/2x21/2 and the budget constraint of p1x1+p2x2=m. Let’s assume that p1=$1.5, p2=$2, and m=$60. Find the optimal bundle. Also, specify the optimal bundle.
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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
Peter's preferences over two goods, x and y, are represented by the utility function u(x, y) = y + 2x. a) Peter is currently consuming bundle A = (2,4) with 2 units of good x and 4 units of good y. Calculate his current level of utility from consuming this bundle. b) Write the expression the indifference curve representing Peter's current level of utility (i.e., the one you found in part (a). Next draw this indifference curve. c) By looking at the indifference curve you drew in part (b), answer the following questions: Does Peter like good x? Good y? Explain. What can you say about the marginal rate of substitution of good x for y, MRSxy? Is it positive? Negative? Constant? Increasing? Decreasing? Interpret/explain your answer in terms of the tradeoffs Peter is willing to make between goods to keep the same utility level. d) On the same graph you drew in part (b), draw the indifference curve for a utility level of 10. Plot and label in the graph bundles B = (1,2), C = (1,6), and D =…
A consumer’s preferences over pizza (x) and steak (y) are given by u(x,y) = x2y (HINT: MUx = 2xy and MUy = x2) and his income is I = $120 and py = $1. (a) Calculate his optimal bundle when pX = $8 (call this bundle A) and separately when pX = $1 (call this point C). (b) Finding the decomposition bundle B, calculate the income and substitution effects on the amount of pizza of a decrease in the price of pizza from pX = $8 down to pX = $1. (c) Forget about the decomposition bundle and the two effects. In (a), the price of pizza decreases, hence the agent ends up better off. Let’s quantify how much “better off” the agent becomes after this price drop, in dollars. For this, instead of the price drop, suppose the agent is given some money $m and he optimize utility with this additional gift included to his budget. What should m be, so that his optimal utility with his expanded budget is exactly equal to his utility at the bundle C (the bundle he chooses optimally when pizza price drops to…