4. (b) There are three people and two goods in an economy. The utility functions and initialbundles are given below:U, = x11X12U2 = 2x21 + x22U3 = X31X32 + X32W1 = (0,8)W2 = (2,2)W3 = (8,0)Suppose it is suggested that the three traders move to the allocation x given by:x1 = (1,2), x2 = (8,4), x3 = (1,4).i) Calculate the marginal rate of substitution for the three at the allocation x.

4. (b) There are three people and two goods in an economy. The utility functions and initial bundles are given below: U₁ = x11x12 W₁ = (0,8) U₂ = 2x21 + x22 W₂ = (2, 2) U3 = X31X32 + x32 W3 = (8,0) Suppose it is suggested that the three traders move to the allocation x given by: x₁ = (1,2), x₂ = (8,4), x3 = (1,4). i) Calculate the marginal rate of substitution for the three at the allocation x.

4. (b) There are three people and two goods in an economy. The utility functions and initial bundles are given below: U₁ = x11x12 W₁ = (0,8) U₂ = 2x21 + x22 W₂ = (2, 2) U3 = X31X32 + x32 W3 = (8,0) Suppose it is suggested that the three traders move to the allocation x given by: x₁ = (1,2), x₂ = (8,4), x3 = (1,4). i) Calculate the marginal rate of substitution for the three at the allocation x.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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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.
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
Suppose you have a $20 gift card and want to buy Blue and Red yarn. The utility function from yards of blue (B) and red (R) yarn can be expressed as follows: U(B,R) = 3B+R Red yarn costs $4 per yard. blue yarn costs $4 per yard. A) Graph the budget constraint and the indifference curves that can be reached. How many yards of each type of yarn will he purchase at these prices with his gift card?
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…
For the case of two goods, give examples of different two utility functions that satisfy all of the following properties: (i) one utility is strictly concave in good 1 and the other is strictly convex in good 2; (ii) they represent the same preferences; and (iii) one utility function is homogeneous of degree 2.