Consider the following utility function:U = 100x.50,0.50A consumer faces prices of P, = $2 and Py =$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 6 units of good X anunits of good Y. Then the marginal rate of substitution is equal to:MRS = 1.83. (Enter your response rounded to two decimal places. Do not forget to include the negative sign.)Use absolute values.The consumer should consumeto maximize utility.more Y and less Xthe same amount of X and Ymore X and less Y15tvMacBook Air80escDIIF1F2F3F4F5F6F7F8@#3%278.QWEYtabs lockASFGHJZCVNMOnteel8 :< COTD

U=100X^0.5Y^0.5 Px=$2 Py=$1 MRS=1.83 MRS is the ratio of marginal utilities of the two goods In a…

Answered: Consider the following utility…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

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Hello, I need assistance in working this through, step by step. I understand the MRS concept, but need help in the algebra to solve it Given the following utility function: U = 100X0.25Y0.25 and marginal rate of substitution: MRS = −0.25Y0.25X A consumer facing the following prices: Px =$10, Py= =$2 chooses to consume: 5 units of good X and13units of good Y. Given this consumption bundle, the marginal rate of substitution is equal to -??(Round your answer to two decimal places. Note that the minus sign is already included.). Given this value, the consumer should consume ▼ more Y and less X the same amount of X and Y more X and less Y in order to maximize his/her utility.
John has a utility function for goods x1 and x2 which is represented by u(x1,x2)=x10.2x20.8. Assume her income is 100 TL and the prices of x1 and x2 are 10 TL and 20 TL, respectively. A) What is the optimal consumption bundle, given income and prices of the two goods? B) How will this bundle change, when all prices double and income is held constant? When all prices double and income doubles? C) Derive the Engel curves.
Given a consumer has a money budget M = 90 and utility function ? ( ? , ?) = ? 1/4? 1 / 2 If she consumes two goods x and y with prices given by ? = 2 and ? = 4 state the ? ? budget constraint equation. Determine the utility maximizing quantities X and Y for the consumer
2)Ben is choosing between cookies and soda. Denote the marginal utility of cookies is MUc, and the marginal utility of soda is MUs. Which of the following relationship is true regarding the marginal utility of substitution (MŘS) of cookie in terms of soda? A) MRS= MUc B) MRS = MUS C) MRS = MUS / MUC D) MRS = MUc / MUs
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).
Question 1 1.1 Explain the principle of a diminishing marginal rate of substitution within the context of consumer preferences and explain the relationship between this principle and the axiom of strictly convex preferences. 1.2 Explain the difference between the ordinal and cardinal approach to utility. Also explain why the ordinal approach will always allow for multiple real-valued utility functions rep- resenting the same underlying (strictly monotonic) preference relations (in other words, explain why using the ordinal approach leads to non-unique utility functions).
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.
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 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? PLEASE ONLY ANSWER PART C, D AND E
John’s preferences for Orange (O) and lemons (L) are represented by the funtion U(O, L)= O+2L. The oranges cost £2 and the lemons £1. Given that John’s monthly income is £30 answer the following questions: What type of goods are oranges and lemons for John? What is the proportion to which John is willing to exchange Oranges for Lemons? Illustrate and solve graphically John’s utility maximization problem. If his income increases every month by £10, how will John’s consumption choice be affected? Illustrate graphically the income expansion path and the Engel curve for each good. How will an increase in the price of Lemons to £6 affect John’s optimal consumption choice? (John’s income is £30) Graph John’s demand curve for each good. Assume that John wins a voucher of £20, redeemable only in Oranges. How would this affect John’s utility? (Assume that prices and income are as described initially) Assume that John is presented with two options: an Orange voucher of £20 or just £6 to spend…
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