Do not use Ai.Answer in all options. Chao's utility function is ♦ = 4��1/2 + ��2.She faces prices ��1 and ��2 and income(a) Write the Lagrangian for Chao's utility maximizationproblem.(b) Use the Lagrangian to solve for the optimalquantities of �1 and ��2 in terms of income andprices.(c) How much income must Chao have to consumeboth goods?

Answered: Chao's utility function is ♦ = 4��1/2 +…

ECON MICRO

5th Edition

ISBN:9781337000536

Author:William A. McEachern

Publisher:William A. McEachern

Chapter6: Consumer Choice And Demand

Section: Chapter Questions

Problem 1.3P

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Take Jeremys total utility information in Exercise 6.1, and use the marginal utility approach to confirm the choice of phone minutes and round trips that maximize Jeremys utility.
Is it possible for total utility to increase while marginal utility diminishes? Explain.
In two commodities world, utility function for a consumer and her income are given respectively. 11 U = x2y2 I= 480 If the price of these goods are Px= 15 and P, = 60 what would be her demand for these two goods * =? and y =? If the price of first good P has increased from 15 to 60. To keep her utility fixed how much does she need to spend for these two goods at least. In other words what should be her minimum income.
Help me with this one
A consumer has the following utility function: Ulx, y) = xy -y, *21 where x and y represents the quantities consumed of goods X and Y. y 20 What will be the substitution and income effects for X and Yassuming that the consumer attempts to maintain the same level of utility achieved before price of Y increased (that is, when price of Y was $1)? SEx= +0.5 IEx = -0.5 SE, = -0.25 IE- = -0.25 SEx= +0.293 IE = -0.293 SEy = -0.414 IE, = +0.414 SEr= +0.25 IE SE, = -0.75 IE, = -0.75 = -0.25 SEx= +0.414 IEx = -0.414 SEy = -0.293 IE, = -0.207 Income = $3 Px= $1, Py= $2
Eren’s two main hobbies are taking vacations overseas (V) and eating expensivemeals (M). His utility function is given as: U(V,M) = V2MLast year, the average price of taking a vacation overseas was US$200 and the averageprice of an expensive meal is $50. However, due to supply problems in Onions, theaverage price of an expensive meal rose to $75. The average price of a vacation did notchange. His income, which is $1500, did not change. Calculate for the equivalent variation (EV) for the price change.
Eren’s two main hobbies are taking vacations overseas (V) and eating expensivemeals (M). His utility function is given as: U(V,M) = V2MLast year, the average price of taking a vacation overseas was US$200 and the averageprice of an expensive meal is $50. However, due to supply problems in Onions, theaverage price of an expensive meal rose to $75. The average price of a vacation did notchange. His income, which is $1500, did not change. Suppose that the Department of Welfare wants to know how much should begiven to Eren to offset his change un utility due to the price increase of an expensivemeal. Calculate the compensative variation (CV).
Eren’s two main hobbies are taking vacations overseas (V) and eating expensivemeals (M). His utility function is given as: U(V,M) = V2MLast year, the average price of taking a vacation overseas was US$200 and the averageprice of an expensive meal is $50. However, due to supply problems in Onions, theaverage price of an expensive meal rose to $75. The average price of a vacation did notchange. His income, which is $1500, did not change. Calculate the change in consumer surplus from consuming the expensivemeals considering the price change (Hint: you need to compare his optimalconsumption bundle before and after the price change to get the change in CS).
Assume Pat spends all of her allowance to purchase 4 apples and 4 candy bars. Pat's marginal utility of the fourth apple is 20 utils, and her marginal utility of the fourth candy bar is 40 utils. If an apple costs $1.00 and a candy bar $0.50, to maximize utility Pat should(A) purchase more apples and more candy bars(B) maintain the current purchase of 4 apples and 4 candy bars(C) purchase more apples and fewer candy bars(D) purchase fewer apples and more candy bars(E) purchase fewer apples and fewer candy bars
4. Consider the utility function U(r,g) r + Iny. (a) Find the marginal rate of substitution. MRS of this function. Interpret the result (b) Find the equation of the indifference curve for this function (c) Compare the marginal utility of r and y. How do you interpret these functions? How might a consumer choose between e and y as she tries to increase utility by, for example, consuming more when their income increases?
An individual’s utility function is given byU = x1√x2where x1 and x2 denote the monthly consumption of two goods. Unit prices of these goodsare $2 and $4 respectively, and the total monthly expenditure on these goods is $300.(a) Write down the budgetary constraint.(b) Find the optimal quantities of x1 and x2 the maximize U.(c) Verify that the stationary point is a maximum.
12. What are the mathematical steps in deriving demand and indirect utility?

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