Consider the following utility function:U= 4X +Y.A consumer faces prices of P, = $2 and P, =1.Assuming that graphically good X is on the horizontal axis and good Y is on the vertical axis, suppose the consumer chooses to consume 10 units of good X and 19units of good Y. Then the marginal rate of substitution (MRS) is equal to:MRS = - 4.00 (Enter your response rounded to two decimal places. Do not forget to include the negative sign.)The consumer should consumeto maximize utility.only good Xonly good Ythe same amount of X and Ytv15МacВook Air80DIIescF1F2F3F4F5F7F8!@#3$%&124789QWYtabASFGH.Kcaps lockCVN Mftcontroloptioncommandつつく0R

Answer: A consumer maximizes his/her utility where the following condition satisfies:…

Answered: Consider the following utility…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Consider the following indirect utility function: V(p,I) = II,( Pi where E-1 a; = 1, and a; + 0 , Vi 1. What's the demand function for x;? (Hint: Take logarithm to both sides of the equation) 2. What's the original utility function? (Hint: If n is too abstract, let n = = 2)
Suppose that Evelyn’s utility function is given as: U(x,y) = xyEvelyn has an income of Php 100. For simplicity purposes, the prices of both goods are equal to one. Following the change in the price of good x, calculate the equivalent variation (EV). (Hint: Use the indirect utility function first to get the new utility level).
A consumer has a utility function U(X,Y ) = X1/2 Y1/2 . Prices of the goods are pX = £10 and pY = £5, respectively, and the consumer has income M = £200 to spend on X and Y. Currently, she buys 2 units of good X and spends the rest of her income on good Y.a) Determine this consumer’s current utility level. b) Compute the consumer’s marginal utilities of goods X and Y. c) Explain why the consumer’s current consumption of goods X and Y is not optimal. Should she substitute X for Y or vice versa? The consumer’s marginal rate of substitution is MRS = Y/X.d) Determine this consumer’s optimal consumption of both goods. e) By how much does the consumer’s utility increase when she consumes the optimal bundle?
Sarge's utility function is U(X1,X2)= X1*X2. If his marginal rate of substitution (MRS) is 3 and he is currently consuming 36 units of good 2, how many units of good 1 is he consuming? [A] Please put your answers in numerical values with no comma or decimal places.
For each of the following utility functions answer the following questions (i-iv): i) Calculate the marginal utilities MUx and MUy ii) Calculate MRSx,y and determine if this is diminishing as good x increases iii) if I=80, Px= 4, Py=2, determine the utility maximizing basket. iv) Determine the demand curves for good x and y (a). u(x,y)= 6x^2/3 +2y (b) u(x,y)= 3x+7y
Joan has the following utility function: u(x, y) = 5x + 3y. Consider that income is I = $8, and prices are given as pa = $4, p = $2. (e) Assume the price of y increases to 4. Find the total, income and substitution effects for x. Consider this price change a "large" price change.
Suppose an individual had a utility function given by: U =X0.6 y 0.8 Calculate this individual's Marginal Rate of Substitution (MRSXY) when they have a bundle with 3 units of Good X and 4 units of Good Y. (Round to the nearest decimal place if necessary.)
A consumer can consume three goods, x₁, x2, and x3. In the markets where she buys them, she is a price-taker and faces prices for the three goods equal to P₁, P₂, and p3, respectively. The consumer has m dollars to spend. Her preferences can be represented by the following utility function: U(x₁, x₂, x3) = x₁x²x². X a) Derive the consumption bundle that maximizes the consumer's utility, subject to her budget constraint. b) Show that the optimal consumption bundle found in part a) is a global maximum. IMG_4479-2.png
Jasper utility function for beer and pizza can be expressed as: U(B,P) = BXP Suppose beer costs $5 per glass, pizzas cost $10 each, and Jasper has a total of $30 to spend. Assume Jaspeer is allowed to purchase fractional amounts of each good. Part A) Based on the above information, what is Jaspeer's optimal amount of beer? Enter the number below. glasses Beer = 3 Part B) Now suppose the price of beer falls from $5 down to $3. Calculate the following and fill in the blanks below. When necessary, round answers to two places after the decimal. (Hint: find the decomposition basket to calculate the substitution and income effects). Jasper's total effect on beer is to increase total consumption by glasses of beer. Jasper's substitution effect is to increase beer consumption by 0.28 Jasper's income effect is to increase beer by 1.12 glasses of beer. glasses of beer.
1. Consider a consumer who consumes two goods. The utility function is given by u(x1, x₂) /2x1+1+√√√x₂, - where x > 0 denotes the amount of good i = the price of good 1 is 3, the price of good 2 is p2 > 0, and the income is 12. 1,2 consumed. Unless stated otherwise, (1) Calculate the marginal rate of substitution (measuring the value of good 1) at the consumption plan (x₁, x₂) = (3, 4). (2) Calculate the consumption plan that is optimal for the consumer. (3) Let v(p₂) denote the utility level at the optimal consumption plan. Calculate its derivative with respect to p2, i.e., v'(P2), at p2 = 3. (4) Suppose that p2 = 1 and the utility level is 10. Calculate the compensated demand for each good.
1) Max chooses to purchase movie tickets and restaurant meals every week with his $100. If the price of a movie ticket is $20 and the price of a restaurant meal is $25, then the slope of his budget constraint will be, a) 1/5 b) -1/5 c) 4/5 d) -4/5 2) Marginal rate of substitution(MRS) is the rate at which consumer is willing to trade one good for another. It must be true that: a) MRS is the slope of an indifference curve in reference to a particular bundle of goods. b) MRS is not the same along an indifference curve that is of usual shape. c) MRS is same along an indifference curve that is of usual shape. d) Both a) and b).
b) As in question 2a, A consumer has a utility function given by U = x°.25 y0.75 and has an income of £100, the price of good x is £5 and the price of good y is £10. Suppose the price of good y falls from £10 to £5. By how much does the demand for good y fall and how much of the resulting change in demand for good y is due to the substitution effect and how much is due to the income effect? Take a picture of your diagrams and upload with your answer

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