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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Sheila decides to take a trip to Peru for her 60th birthday. She looks forward to the guided tours (T) and the food (F). She is allocating $2,000 to spend on guided tours and food. Sheila's preferences over these two goods T and F is represented by the utility function: U(F, T) = = √F+T Denote prices for tours and food as på and pf, respectively, and take them to be pt = $100 and PF = $20. a. Carefully draw at least two indifference curves to get a sense of Sheila's preferences. Are Sheila's preferences "well-behaved"? [Note: Go ahead and put T on the y-axis and F on the x-axis so that your pictures are consistent with mine.] b. Derive an expression for Sheila's marginal rate of substitution. What is the MRS in words? What does her MRS approach as F→ 0? How about when F→→∞o? How do you interpret these findings, in words? c. In the above analysis, you found that Sheila's MRS does not depend on T. Please show what it means for the MRS to be independent of T either in a new graph in the…
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).
For the utility function U = Qx0.31 (1-0.31) and the budget 114 = 9Qx+8Qy find the CHANGE in optimal consumption of Y if the price of X increases by a factor of 2.0. Please enter your response as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 = 1.2, 1.14 = 1.1).
Suppose your utility for goods x1 and x2 is represented by the following utility function: U(x1,x2)= x11/5 x24/5 a) What is your marginal rate of substitution, MRS12? b) If the price for good x1 is p1 = 2, the price for good x2 is p2 = 4, and your available income is m = 20, write down your budget constraint. c) Using the prices and income given at b) above, find your optimal consumption choice bundle (Marshallian demand) and its corresponding utility level. d) Illustrate your optimal consumption choice on a graph. e) For the prices given in b), what income would you need to achieve a utility level of 25?
Suppose the preferences of an individual are represented by a quasilinear utility function: U(x, y) = In(x) + 3y a) Initially, Px=1, Py=6 and 1=102. Then, the price of x increases to 2 (Px=2). Calculate the changes in the demand for x. Please also calculate the substitution and income effects of the change in Px on x. (Hint: since the change in price is not small, you cannot use the Slutsky equation. You need to have numbers instead of functions as the answer.) B)Please also calculate the substitution and income effects of the change in Pr on y. C) Instead of doubling to 2, suppose Px is only increased by a small amount. Use the Slutsky equation to find the substitution and income effects of the change in the price of x on x. Compare your result to (a). Explain why there's no income effect of the change in Pa On X. Show your result on an indifference curve. d) Use the Slutsky equation to find the substitution and income effect of the change in Px on y. Compare your result to (b).
For the utility function U = Qx0.28Q (1-0.28) and the budget 137 = 11Qx+6Qy find the CHANGE in optimal consumption of X if the price of X increases by a factor of 1.6. Please enter your response as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 = 1.2, 1.14 = 1.1).
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
For the utility function U = Qx0.46Qy(1-0.46) and the budget 100 = 11Qx + 11Qy find the CHANGE in optimal consumption of X if the price of X increases by a factor of 1.5. Please enter your response as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 = 1.2, 1.14 = 1.1).
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.

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