Given the utility function U ( X , Y ) = X 1 3 Y 2...

Given the utility function U ( X , Y ) = X 1 3 Y 2 3, find the absolute value of the MRS when X=10 and Y=24. Round your answer to 4 decimal places.

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Rahul Sunny answered 2 years ago

Suppose a consumer's utility function is given by U ( X , Y ) = X...

Suppose a consumer's utility function is given by U ( X , Y ) = X 1 2 Y 1 2. The price of X is PX=8 and the price of Y is PY=5. The consumer has M=80 to spend. You may find that it helps to draw a graph to organize the information in this question. You may draw in the blank area on the front page of the assignment, but this graph will not be graded. a) (2...

Assume a Cobb-douglas utility function of 2 goods x and y given by U = x...

Assume a Cobb-douglas utility function of 2 goods x and y given by U = x 0.5y 0.5 and an initial income I of 100. Let initial price be px = 4 and py = 1. Now vary the price of x from 1 to 7 in steps of 1. So you have 7 prices for x. px = {1, 2, 3, 4, 5, 6, 7} For each of these px, py REMAINS the SAME at 1. In the excel...

Jim’s utility function is U(x, y) = xy. Jerry’s utility function is U(x, y) = 1,000xy...

Jim’s utility function is U(x, y) = xy. Jerry’s utility function is U(x, y) = 1,000xy + 2,000. Tammy’s utility function is U(x, y) = xy(1 - xy). Oral’s utility function is -1/(10 + xy. Billy’s utility function is U(x, y) = x/y. Pat’s utility function is U(x, y) = -xy. a. No two of these people have the same preferences. b. They all have the same preferences except for Billy. c. Jim, Jerry, and Pat all have the same...

1. Given the Utility function U(X,Y) = X.5 + Y.5 a. Write mathematical expressions for marginal utility of...

1. Given the Utility function U(X,Y) = X.5 + Y.5 a. Write mathematical expressions for marginal utility of x and marginal utility of y b. Does the consumer the assumption of non-satiation (more is better) desire more of x and y? c. If the quantity of Y is held constant, does the marginal utility of x increase, remain constant or diminish as x increases? Prove your answer d. Derive an expression for the marginal rate of substitution of x for y. e. If Price of X...

An individual's utility function is U= (X+1)0.5 (Y+2)0.5

An individual's utility function isU= (X+1)0.5 (Y+2)0.5(a) By implicit differentiation, find the slope of any indifference curve and show that it is given by the ratio of marginal utilities of the two goods.(b) Find the indifference curve for U= 6 and show that it is negatively sloped and convex. Does the indifference curve cut the axes? What does this imply about this individual's tastes?

An individual utility function is given by U(x,y) = x·y1/2. This individual demand equation for x...

An individual utility function is given by U(x,y) = x·y1/2. This individual demand equation for x is a factor a of I/px: x* = a (I/px). In this specific case, factor a is equal to ______. (NOTE: Write your answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Add a leading zero and trailing zeros when needed.)

A consumes two goods, x and y. A ’s utility function is given by u(x, y)...

A consumes two goods, x and y. A ’s utility function is given by u(x, y) = x 1/2y 1/2 The price of x is p and the price of y is 1. A has an income of M. (a) Derive A ’s demand functions for x and y. (b) Suppose M = 72 and p falls from 9 to 4. Calculate the income and substitution effects of the price change. (c) Calculate the compensating variation of the price change....

Suppose a consumer has a utility function given by u(x, y) = x + y, so...

Suppose a consumer has a utility function given by u(x, y) = x + y, so that the two goods are perfect substitutes. Use the Lagrangian method to fully characterize the solution to max(x,y) u(x, y) s.t. x + py ≤ m, x ≥ 0, y ≥ 0, where m > 0 and p < 1. Evaluate and interpret each of the multipliers in this case. What happens to your solution when p > 1? What about when p =...

Suppose Anne’s utility function for food (X) and clothing (Y) is given by U (X,Y) =...

Suppose Anne’s utility function for food (X) and clothing (Y) is given by U (X,Y) = 4X1/2 + Y and Anne had budget constraint I = PxX + PyY. a. Find Anne’s optimal bundle if Px = 4 and Py = 4 and Anne has I = 60. b. Discuss how the demand for X depends on her income. c. Suppose now that the price of X increases to 8. Find the SE and IE of the price change.

Chepa’s utility function is given by U (x, y) = ln x + 4 ln y....

Chepa’s utility function is given by U (x, y) = ln x + 4 ln y. Assume that Chepa has endowments (10, 10) and that Py = 10 throughout the problem. (h) This part of the question is to investigate Chepa’s welfare under different prices. We will do it step by step. (i) By substituting out the M with the expression of Chepa’s endowment income (see part (g)), obtain Chepa’s gross demands as functions of Px. (ii) Plug your answer...

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