Suppose you find that MU₁(x₁+x₂)=2x2 and MU₂(x1,x2)=2x1. What is the rate at which the consumer is willing to trade good 2 for good 1 at bundle (2,4)? (Note: enter a positive number, i.e. enter the quantity of good 2 that the consumer is willing to give up for an additional marginal-unit of good 1.) Question 21 Suppose a consumer is always willing to give up 5 units of good 2 for an additional unit of good 1. For this consumer. Good 1 and good 2 are perfect complements Good 1 and good 2 are perfect substitutes Good 1 and good 2 are both essential goods None of the above

Suppose you find that MU₁(x₁+x₂)=2x2 and MU₂(x1,x2)=2x1. What is the rate at which the consumer is willing to trade good 2 for good 1 at bundle (2,4)? (Note: enter a positive number, i.e. enter the quantity of good 2 that the consumer is willing to give up for an additional marginal-unit of good 1.) Question 21 Suppose a consumer is always willing to give up 5 units of good 2 for an additional unit of good 1. For this consumer. Good 1 and good 2 are perfect complements Good 1 and good 2 are perfect substitutes Good 1 and good 2 are both essential goods None of the above

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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1. Consider a consumer who consumes two goods. The utility function is given by u(x1, x₂) /2x1+1+√√√x₂, - where x > 0 denotes the amount of good i = the price of good 1 is 3, the price of good 2 is p2 > 0, and the income is 12. 1,2 consumed. Unless stated otherwise, (1) Calculate the marginal rate of substitution (measuring the value of good 1) at the consumption plan (x₁, x₂) = (3, 4). (2) Calculate the consumption plan that is optimal for the consumer. (3) Let v(p₂) denote the utility level at the optimal consumption plan. Calculate its derivative with respect to p2, i.e., v'(P2), at p2 = 3. (4) Suppose that p2 = 1 and the utility level is 10. Calculate the compensated demand for each good.
Please help me to solve questions (a) (b) (e). (especially question e). thank you!
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Which of the following statement is TRUE based on this question : A utility function with 2 goods (X,Y) is given by U = X^1/2Y. If there’s 3 bundles, bundle A = (9,3); bundle B = (4,1); bundle C = (16, 4)
Give only typing answer with explanation and conclusion to all parts Martina’s preferences are represented by u(x , x ) = x2 + x3 , where x > 0, x > 0. (1) What is the marginal utility of good 1 at (x1, x2)? (2, 3)? (2) What is the marginal utility of good 2 at (x1, x2)? (3, 2)? (3) What is the marginal rate of substitution of good 2 for good 1 at (x1, x2)? (2, 2)? (4) Redo (1),(2),(3) for another representation v(x1,x2)=ln(x^1/2 +x^(1/3).)
Suppose you find that MU1(X1Xx2)=2x2 and MU₂(x1+x₂)=2x1. What is the rate at which the consumer is willing to trade good 2 for good 1 at bundle (2,4)? (Note: enter a positive number, i.e. enter the quantity of good 2 that the consumer is willing to give up for an additional-marginal-unit of good 1.) Question 20 Suppose you find that the expressions of the marginal utilities for a consumer are given by MU1 (1,2)= 2 and MU₂ (1,2)= 7. Then you can conclude that: This consumer has Cobb-Douglas tastes For this consumer good 1 and good 2 are perfect complements For this consumer good 1 and good 2 are perfect substitutes None of the above Question 21 Suppose a consumer is always willing to give up 5 units of good 2 for an additional unit of good 1. For this consumer: Good 1 and good 2 are perfect complements Good 1 and good 2 are perfect substitutes Good 1 and good 2 are both essential goods None of the above
2(b)There are three people and two goods in an economy. The utility functions and the initial bundles are given below: U1 = X11X 12 U = 2x 21+ X 22 U3 = X 31 X 3z+X 32 W; = (0,8) W;= (2,2) Wy= (8,0) Suppose it is suggested that the three traders move to the allocation x given by x;= (1,2), x2= (8,4), X3= (1,4) b. Show that x makes no one worse off than the original allocation.
1.2 Ann and Bob each own 10 bottles of beer and, altogether, they own 20 bags of peanuts. There are no other people and no other goods in the economy, and no production of either good is possible. Using a to denote bottles of beer and y to denote bags of peanuts, Ann's and Bob's preferences are described by the following utility functions: UA (XA, YA) = TAYA and UB (XB, YB) = 2xB+ YB. In each of the following cases, determine the market equilibrium price ratio and allocation and depict the equilibrium in an Edgeworth box diagram. (a) Bob owns 20 bags of peanuts and Ann owns no peanuts. (b) Bob owns 15 bags of peanuts and Ann owns 5 bags. (c) Ann owns 20 bags of peanuts and Bob owns no peanuts.
9) The satisfaction obtained by a consumer of good 1 and good 2 can be represented by the utility function u (X1, X2) = X1 + 2X2 If the price of good 1 is p1 = 2 and the price of good 2 p2 = 3 its income is positive, then Choose one: A)The consumer will demand a positive amount of good 2 and will not demand anything good 1 B)The consumer will demand) a positive amount of good 1 1 will not demand anything good 2 C)The consumer will demand a positive amount but not necessarily the same amount of both goods. D)We cannot make any statement as to the quantity demanded of each good E)The consumer will demand an equal (positive) amount of both goods
(2) Graph the following given these two goods and their respective prices: books (units with per week) at price Ph=1; and food (units per week) at price Pƒ= 2: (a) Point A (market basket A) that maximizes satisfaction of a consumer. (b) Point B (market basket B) that is affordable but satisfaction is not maximized. (c) Point C (market basket C) that gives a higher level of satisfaction but not affordable.
5) A consumer of two goods, good 1 and good 2, has a utility function u (X1, X2) = x1 0,6. X2 0,4, where x denotes units of good 1 and X2 units of good 2. The price of good 1 is 5 euros And the price of good 2 is 3 euros per unit and the consumer’s income is 150 euros. Suppose that only the price of good 1 changes and that the new price is p, ‘ = 2. Then the demand function of good 1 that is derived from the utility function is Choose one: A) X1= 0.6m/p1 B) X1= 6m/p1 C) X1= 4m/p1 D) X1= 0.4m/p1 E) Not defined
Part A . Consider an economy with the following features. • There are 100 identical consumers that derive utility from consuming three different goods: software, computers, and good m. • Each consumer decision utility function is given by U (c, 8) = 4c¹/48¹/4+m, where e denotes the amount of computers that she consumes, s denotes the amount of software that she consumes, and m denotes the amount of good m that she consumes. cand s must be non-negative, but m can take any real value. • Computers are produced by 20 identical competitive firms with a total cost function given by 10c². • Software is produced by 40 identical competitive firms with a total cost function given by 20s². . QUESTION 1: What are the equilibrium prices for software and comput- ers in equilibrium? Part B • Suppose that there is a positive technology shock in the software industry so that that the new cost function of the software firms becomes 10s². Let C and S denote, respectively, the aggregate level of…