Calculate the MRS for the following utility function $ U(x_1, x_2) = 2x_1^2 + x_2^2 + e^{3x_1} $ (in text mode, the function is 2x1^2 + x2^2 + e^(3x1)) and explain whether it satisfies the property of diminishing MRS.

Utility function : U(x1 , x2 ) = 2x12 + x22 + e3x1 Marginal Rate of substitution refers to the rate…

Answered: Calculate the MRS for the following…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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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.
Imagine Billy eats brownies (B) and cookies (C) and considers them to be perfect substitutes. Brownies yield him four times more utility than cookies. Which of the following equations could describe his utility function? U= 0.25B + C O U=B+ 0.25C U = B'C OU = BC4 %3D
Please refer to the following information to answer the question (in bold) below: You enjoy consuming apples (A) and oranges (O). Suppose that your utility function over both goods is given by Your marginal utility function for apples is . Your marginal utility function for oranges is U (A, O) = AO³ MUA = 0³ MUO 3A0² . Currently, the price of apples is $10/peck, the price of oranges is $5/pound, and your income is $160. Assume that apples are your horizontal axis good and oranges are your vertical axis good. = When you set up the optimal decision rule for your consumer problem, which of the following statements best describes how much you will buy of apples and oranges at your consumer equilibrium? For each peck of apples, you will buy 1/3 pounds of oranges. For each peck of apples, you will buy 1 pounds of oranges. O For each peck of apples, you will buy 3 pounds of oranges. O For each peck of apples, you will buy 6 pounds of oranges.
What is the optimum solution for this utility functions? • U= min (1/2x, 1/2y) • U= 1/2 x +1/2 y • -U= In x + y Explain why non-convex IC has a corner solution instead of an interior solution?
Derive Ryan's demand function for q₁, given his utility function is where o = = (9₁) P + (9₂)P, 1 1-p The demand curve for q₁ as a function of P₁, P2, and Y is (Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a subscript can be created with the_ 9₁ = character.) U= Let the price of q₁ be p₁, let the price of q2 be p2, and let income be Y.
Laura's preferences over commodities X₁ and x₂ can be represented by U(x₁,x2)=min{3x₁, x₂}. She maximizes her utility subject to her budget constraint. Suppose there is an increase in p1. There are both income and substitution effects of this price change. There is an income effect but not a substitution effect of this price change. There is a substitution effect but not an income effect of this price change. It is unclear whether the consumer will buy more or less x1 as a result of the increase in p1.
Suppose the function for the utility from good c is denoted as U(c)=2c1/2 . Which of the following expressions indicates the marginal utility of c?

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Calculate the MRS for the following utility function U (x1, X2) = 2x + x; + e³x1 (in text mode, the function is 2x1^2+x2^2+e^{3x1}) and explain whether it satisfies the property of diminishing MRS?