Suppose we have the following utilityfunction: U(x,y)=x^O.33 y^0.671) What is the Marginal utility of x? Marginalutility of y?2) Comment on how the marginal utility ofeach changes as x increases and discusswhy that makes sense.3) Does this utility function follow the moreis better rule? How do you know?4) What is the marginal rate of substitution(MRS)? What do we know about the shapeof the indifference curve given this MRS?5) Now suppose we have a new utilityfunction: U(x,y)=x+y. What type of goodsare these? Explain.

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Answered: Suppose we have 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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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 the utility function for goods x and y is given Utility = U(x,y) = xy +y Suppose price of both x and y is $1. You have total $10 to spend. Suppose price of x changed to $0.5. Price of y and your disposable income remain the same: a. calculates the change in the amount of good x, that is caused by the substitution effect (the effect on consumption due to a change in price holding real income or utility constant). b. calculate the change in the amount of good x, that is caused by the income effect (the effect on consumption due to a change in real income caused by a change in price).
Consider a consumer with preferences over two goods, x and y. Preferences are given by U(x,y) = xy. Suppose the consumer’s income is $72 and the price of good y is $1. Suppose the price of good x is initially $4 and subsequently rises to $9. Find the numerical values of the income and substitution effects on the consumption of good x
What is the marginal rate of substitution (MRS) for the utility function U(x, y) = x° + yP? The marginal rate of substitution of good x for good y is MRS = (Note: Be sure to use the Greek letter rho provided in the tool palette in your response.)
a) Explain by using an example why an MRS (Marginal Rate of Substitution) between two goods must equal the ratio of the price of the goods for the consumer to achieve maximum satisfaction?
3. The utility that Elena receives by consuming food F and clothing C is given by U(F, C) = FC + F. Food costs £1 per unit, and clothing costs £2 per unit. Elena's income is £22. MUF = C+1 and MUc = F. (i) Define the term Marginal Rate of Substitution (MRS) (ii) Find the utility maximizing values of C and F for the numerical values given above (Hint: You can assume interior solution). (iii) Now suppose that price of C and Elena's income remain unchanged at £2 per unit and £22, respectively, while the price of F varies. Find the equation of the demand for F as a function of the unit price of F (PF).
For the Cobb-Douglas utility function: the income and substitution effects are necessarily the same size. there is only an income effect, no substitution effect. there is only a substitution effect, no income effect. the demand for each good is independent of changes in the price of the other good.
Diminishing marginal rate of substitution for a good means: I. decreasing the quantity of a good that the consumer would give up for one more additional quantity of the other good II. increasing the quantity of a good that the consumer would give up for one more additional quantity of the other good III. no change for the quantity of a good that the consumer would give up for one more additional quantity of the other good IV. all answers are correct
Q.7 A consumer's utility function is given by the expression: U = (0.6A"' + 0.47'"s} Determine the marginal utility functions for each commodity. Does marginal utility decrease when consumption increases? Assuming that the price of good X is Rs 15 and the price of Y is Rs 6, write the equation of the budget line and plot it when income is Rs 450. What is its slope? What does it indicate? Calculate the marginal rate of substitution of Y for X and interpret its economic meaning. Write the equation showing consumer's equilibrium condition. Obtain the equilibrium values of X and Y. Find the expressions for change in MUx due to increase in Y and change in MUy due to increase in X.
Can you help me answer this macroeconomics theory question
Consider the single-good utility function u(x) = 3x². du(x) a) Find the marginal utility of x, MUx = dx b) Plot the utility function and marginal utility function on two separate graphs. c) Does this utility function satisfy the law of diminishing marginal utility? Explain.
8. Fabian consumes X and Y and the following utility function represents his utility: U = 2XY a. With a utility function of U = 2XY, Fabian's MU, = 2Y and his MU, = 2x ,where MU is marginal utility. Write an equation for Fabian's marginal rate of substitution (MRS). b. Suppose Fabian's income is $120 and Px = S6 and Py-$2, where Px is the price of X and Py is the price of Y. Write an equation for Fabian's budget constraint. c. Write the equation that equates the slope of Fabian's budget constraint to the slope of Fabian's indifference curve: d. If Fabian is spending all of his income, how much X and how much Y will he choose? Use the equations you wrote in part's b and c to answer this question. e. What will Fabian's utility be with this combination of X and Y? f. Now suppose the price of X increases to P.=10. Write the equation that equates the slope of Fabian's budget constraint to the slope of Fabian's indifference curve. How will this change the optimal combination of X and Y? What…

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