Show that the two utility functions given below generate identical demand functions for goods X and YUCXY) log(X)+log(YC) UCxY) (XY05The demand function for good X and the demand function for good Y for both utility functions equalO A.X=and YPvPxО В.Х-and Y2PvОс.X Y=21PXPYO D.Х-and Y2P.2PyОЕ.X= Y=РХPY

Two utility functions are given which are:

Answered: Show that the two utility functions…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Similar questions

Which of the following correctly defines compensating variation? O The difference in the price a consumer is willing to pay and the price the consumer actually pays. The amount of income that a consumer requires to compensate them for a lower quality product. O The amount of income that must be given or taken away from a consumer to keep their purchasing power constant after a price change. O The amount of income that must be given or taken away from a consumer after a change in price, such that their welfare after the price change is the same as it was before the price change. O The amount of income that must be given or taken away from a consumer before a change in price, such that their welfare before the price change is the same as it will be after the price change. O No answer.
A very large substitution effect of a price change (relative to the magnitude of the income effect) implies a relatively flat demand curve. O True O False
When goods are complements, there is a direct relationship between the price of one and the demand for the other. O 1) True O 2) False
The figure to the right represents the demand for ice cream cones. Which of the following statements is true? O A. Points a and b may not necessarily be the utility - maximizing quantities of ice cream cones at two different prices because we have no information on the consumer's budget or the price of other goods. B. Points a and b are the utility - maximizing quantities of ice cream cones at two different prices of ice cream. O C. Points a and b are derived independently of the utility - maximizing model. O D. Point a could be a utility - maximizing choice if the price is $3 but point b may not be because we have no information on the marginal utility per dollar when price changes. Price $3 1 3 4 Demand Quantity
Q1
am. 130.
X2 Phil has preferences over olives (x₁) and ice creams (x₂) with a utility function, u(x₁, x₂)= x₁0.5+ x₂0.5. Suppose his income is $16 and the price of olives is $1 and the price of ice creams is $1, too. Which of the following is TRUE? O The utility level when he spends all of his income on good 1 is 8. O The optimal bundle Phil will choose to consume is (6,10). O The utility level at a bundle (1,16) is 11. None of the above. The optimal bundle Phil will choose to consume is (8,8).
2 3 1. The consumer has Cobb-Douglas preferences for two goods x and y: u(x, y) = 10x¾yš Py> 0 and m > 0 is given. a) Set up the Expenditure Minimization Problem. b) Calculate MU and MUy. Ꮖ c) State the condition that explain why Cobb-Douglas preferences will guarantee an interior solu- tion. c) Give the two optimality conditions for x and y. i) ii) Px > 0, e) Solve for the compensated demand functions for good x and y.
1. Let Amy derive utility each from housing, h, and a consumer good, z, with the following utility function: 1/ U=h¾/3₂¾3 M Her Mashallian demand equations are the following: h= and z=- 3ph 2M 3p₂ Amy lives in a city where everyone works downtown. While her income is $160 per month, her commute cost (bus pass) costs her $40 per month, so she only has $120 to spend on h and z. (we assume no time cost of the commute) The consumer good, z, has a price of $1 and the price of her housing, h, is $2 per unit. a. What is her quantity demanded of h and z and what level of utility is she currently enjoying? She is considering moving to a location further from work to a house where her commuting cost would be $60 per month (so she will have $100 to spend on z and h). The market adjusts ph and housing sizes across the city so that utility is the same at every location around the city. b. What is the equation for the appropriate demand function for housing in this city? C. What the price of housing…

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