Consider a consumer whose preferences can berepresented by the utility function u(x, y) = x + y(a) Originally, px = 1, py = 2 and m = 1. Whatbundle does the consumer choose,and what is his utility from this bundle?(b) The price of good x then rises to 3. Whatbundle does the consumer choose after the pricechange, and what is his utility from this bundle?(c) Calculate the compensating variation. (Hint: atthe new price ratio, what good will he spend hisincome on?)(d) Calculate the equivalent variation.

utility function measures the welfare or satisfaction of a consumer as a function of the consumption…

Consider a consumer whose preferences can be represented by the utility function u(x, y) = x + y Ca) Originally, px = 1, py = 2 and m = 1. What bundle does the consumer choose, and what is his utility from this bundle? b) The price of good x then rises to 3. What

Consider a consumer whose preferences can be represented by the utility function u(x, y) = x + y Ca) Originally, px = 1, py = 2 and m = 1. What bundle does the consumer choose, and what is his utility from this bundle? b) The price of good x then rises to 3. What

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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The price of goods A and B are 20 and 10 respectively. given that the marginal utility of commodity A is 10. what is the marginal utility of B if the consumer is at equilibrium.
2. Ping receives a weekly allowance to purchase soda (x) and juice (y) at school. His preferences over these two goods can be represented by the utility function U(x,y) =0.5x+ 5lny where x represents the number of cans of soda and y represents the number of juice boxes. a) Given his preferences find his Marshallian demand functions for soda (x) and juice (y). b) Suppose that the price of a can of soda is $1.5 and that Ping has $30 to spend on soda and juice. Write Ping's demand curve for juice (y). Illustrate his demand curve. c) Suppose that the price of a box of juice is $1 (the price of soda and income remain $1.5 and $30, resp.). Use your demand functions to find his best bundle. In an indifference curve diagram illustrate his best bundle at these prices. For the remainder of the question assume that Ping's allowance (income) rises to $36 per week and the prices of the two goods are unchanged at Px= $1.5 and Py= $1. d) Use your demand functions to find his new best bundle. e)…
compute the marginal utility of good X (MUX) and the marginal utility of good Y (MUY).a. U=U ( X ,Y )=3 X1 /2+5Y1/ 2
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Alice is going to Wonderland and needs supplies. She has $100 and can buy only walnuts and raisins. The price of walnuts is $20 per kg and of raisins is $10 per kg. Alice's preferences are described by the utility function u(x1,x2)=min{0.5*x1+2*x2,x1}, where x1 is the quantity of walnuts, and x2 is the quantity of raisins. Given her budget constraint and preferences, if Alice were offered a choice only among the bundles listed below, which one would she buy? Выберите один ответ: a. x1=3, x2=4 b. x1=2, x2=0.5 c. x1=4, x2=3 d. x1=1, x2=8
Solve these consumer choice problems: a. Suppose a consumer has a utility function u(x, y) = xy + 7y facing prices p,=S1 and p,=$2 and income I = $10. Draw a diagram and find the consumer's optimal consumption of goods x and y. b. Suppose that you are in a situation where you can afford purchasing 3 units of good x and 4 units of good y. You discover that another affordable bundle of 5 units of good x and 2 units of good y causes you to reach the same level of utility. Assume that your utility function and budget line are both well behaved. Are you maximizing your utility by consuming your original bundle? Why or why not? Propose an alternative, affordable bundle that would yield a higher utility level than either of the original bundles.
4. Tim wants to maximise his utility given his utility function of U (A, B) = A² B¹. He faces the following prices and income: PA = 25; PB = 20; M = 250. However, a change in the price of good A to PA 22 will change his optimal bundle. If he is only interested in being able to consume his original bundle of goods, how much income would he need after the price change? = (a) Tim would require £54 less income (b) Tim would require £18.33 more income (c) Tim would require £10 less income (d) Tim would require £16.66 more income (e) Tim would require £16.66 less income
1. In a simple but delicious world, Joey eats only sandwiches, s, and jam, j. He has a Cobb-Douglas utility function U(j, s) = Nj1-asª, where 0 0. The price of jam is pj, the price of sandwiches is Ps, and Joey has a monthly budget Y to spend on lunch. a. Explain why you can safely use a simpler Cobb-Douglas utility function, V(j, s), to represent Joey's preferences, which is the same as U(j, s) except for replacing N with 1. b. Transform V(j,s) by taking natural logs and bringing down exponents. Explain why it is useful to do this for a Cobb-Douglas utility function, but not for a quasi-linear utility function. Use In(V(j, s)) and the substitution method to derive the formulas for Joey's optimal amount of jam, j*, and sandwiches, s*, to buy and consume per month. Simplify your answers so that you arrive at the С. (1-a)Y aY formulas j* = and s* Ps d. What fraction of his income does Joey spend on jam, and what fraction on sandwiches?
b. A consumer purchases two goods, the amounts of which are x and y. Her marginal utility of consuming good x is Ux , while that of consuming good ? is Uy. If the two marginal utility functions are given by Ux = y2 + 2xy and Uy = 4xy + 3x2 − 3 and the consumer is known to stay on the same utility curve, find the total utility function of this consumer buying the two goods
2. Suppose there are two goods in the economy: Food (F) and Composite good (Y), with Pp = 1 and Py = 2. Consider a consumer who has utility function u(F,Y) = InF + In Y and income I = $100. (a) Find the consumer's consumption choice. (b) Suppose, to promote better nutrition, the government institutes a welfare program that gives every consumer with income less than $500 additional $100. Find the consumer's new consumption choice. How much of the government's payment went into purchasing Food? (c) Suppose rather than giving cash, the government gives a voucher that can only be used to purchase (up to) $100 worth of Food. How does this affect the consumer's consumption choice? (d) Which of the two programs is more effective in achieving the government's goal? Explain.
Consider a consumer whose utility function is (screenshot) Assume the consumer has income $120 and initially faces the prices px=$1 and py=$1. How much x and y would they buy? Draw the budget constraint and the demands.
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