Show full answers to part d) e) f) Exercise 3Maria is a consumer with preferences over good x and good y representedby the utility function u(x, y) = x²y. The price of good y in this market is Py = $2.a) Derive Maria's demand functions of good x and good y. [Hint: Solve the UMP keepingPx and I undefined and using py = $2]b) Draw her demand curve of good x assuming she has an income of I = $240.c) On a separate graph, draw her Engel curve for good y. Is good y a normal good forMaria? Explain.Jim is another consumer buying on the same market as Maria. His preferences over the two goodsare represented by u(x, y) = xy. Since he is on the same market, he is facing the same prices asMaria does.d) Derive Jim's demand functions of good x and good y. [Hint: Solve the UMP keeping Pxand I undefined and using py = $2]e) Draw his demand curve of good x assuming he has the same income than Maria, I =$240. Use the same price levels you used for plotting Maria's demand curve in part (b).f) Derive the aggregate market demand function of good x when Maria and Jim are theonly two consumers on the market. Next, on a separate graph, draw the market demandcurve of good x.

The utility is the total satisfaction that the consumer gets from the consumption of a good .The…

d) Derive Jim's demand functions of good x and good y. [Hint: Solve the UMP keeping Px and I undefined and using py = $2] e) Draw his demand curve of good x assuming he has the same income than Maria, I = $240. Use the same price levels you used for plotting Maria's demand curve in part (b). f) Derive the aggregate market demand function of good x when Maria and Jim are the only two consumers on the market. Next, on a separate graph, draw the market demand curve of good x.

d) Derive Jim's demand functions of good x and good y. [Hint: Solve the UMP keeping Px and I undefined and using py = $2] e) Draw his demand curve of good x assuming he has the same income than Maria, I = $240. Use the same price levels you used for plotting Maria's demand curve in part (b). f) Derive the aggregate market demand function of good x when Maria and Jim are the only two consumers on the market. Next, on a separate graph, draw the market demand curve of good x.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter3: Preferences And Utility

Section: Chapter Questions

Problem 3.7P

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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
1. John spends PLN 60 per week on two goods: x and y. The price of good x is PLN 2 and the price of good y is PLN 6. The utility function is: U(x, y) = x² + y a) What quantities of products x and y does he purchase each week at equilibrium? b) What will happen if Piotr's income increases by PLN 6 per week? What will be the new demand for x and y?4
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.
Show full answers to part a) & b)