QUESTION 1Alice (A) and Bob (B) have an endowment of goods 1 and 2, with Alice's endowment being (wt, w) = (1,2) and Bob's endowment equals(wf , w) = (1,3). Alice's utility is given by u4 (xf, xf) = 2 ln xf + In æ£ , while Bob's utility is uB(xf, x}) = ln xf + 2 ln x? .Suppose that the social planner considers it to be imperative that agent B consumes exactly one uniof good 1 and four units of good 2. Although the social planner can not force the individuals to a particular consumption, they can enforcetransfers of good 1 between the consumers (transfers of good 2 are not enforceable by the social planner). What transfer of good 1 wouldguarantee that in the resulting competitive Walrasian equilibrium consumer B consumes one unit of good 1 and four units of good 2?Answer this pleaseSelect one:O a.One half unit of good 1 has to be transferred from agent A to agent B.O b.There is no endowment for which agent B would consume x= 1 and x = 4 in the corresponding competitive equilibrium.Therefore, no such transfers exist.О с.One unit of good 1 has to be transferred from agent A to agent B.O d.Transferring good 1 is not sufficient. It is necessary to transfer one unit of good 2 from agent A to agent B.

Walrasian equilibrium: It is theory that explains the macroeconomy functions as a whole. It do not…

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ENGR.ECONOMIC ANALYSIS

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Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

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Consider an Edgeworth-box economy, which contains two individuals i and j, and two goods (and 2. The total endowment of good I is 8, and the total endowment of good 2 is 4. Individual i has the Leontief utility U₂C X₁, X₁z) = min (X₂₁, Xiz) for all X₁, Xiz 20, while individual j has the Linear utility U₁ (Xj₁, Xj₂)=Xj₁t Xj₂ for all X₁, Xyzzo, which allocation below this is not Patreto efficient / optimal a. (( X ²1, Xit), (X₁₁ + X₁²₂)) =((2, 2), (6,2)) 6. (( X ₂₁, Xiv), (X; ₁ ; X₁3₂)) = (C0₁0), (814)) c. (CX₁, Xt₂), (X3³₁, X₁₂)) = (( 8₁4), (0, 0)) d. ((x), X₁₂), (X₁, X3₂)) =((4,4), (4,0))
Consider an economy with 2 goods and 2 agents. The Örst agent has the utilityfunction, u (x1; x2) = ln x1 + 2 ln x2, and the other one has u (y1; y2) = 2 ln y1 + ln y2.The aggregate endowments of the 2 goods are given by (50; 100). Suppose there is asocial planner who cares about agents equally.(a) Set up the plannerís problem b) Calculate the first-best outcome (i.e., the social plannerís solution).
Two individuals A and B have utility functions defined over two goods, a private good 'x') and a public good, 'F. The utility function of an agent 'i' is defined by ui = 2 log xi + log F where F =FA + FB. Each agent has 200 units of private goods x, as his endowment and 1 unit of private good can be transformed into 1 public good F. Answer the following (a) Find the Nash equilibrium values of FA and FB? (b) What is the Pareto optimal level of F? (c) In what condition the Pareto optimal level of F will not depend on the number of private goods? (d) What would be the consumption of x by each agent if they contribute equally towards the public good (F)? (e) Would it change if an agent had a larger endowment of x to begin with?
(5) A has utility function u4(x4) = x4 + x and initial endowment w4 = (3,6). Consumer B has utility function uB (xB) = xf · x% and initial endowment wB = (3,6). Consider an exchange economy with two consumers and two goods. Consumer (a) Is the initial endowment a Pareto efficient allocation? Justify your answer. (b) Find a competitive equilibrium (p, xª, x³) for the economy. (c) Construct the contract curve. A picture here is not a complete answer; you need to specify analytically the set of points that are in the contract curve.
Consider the following pure exchange, Edgeworth box economy. There are two consumers, Adam and Mark, and two goods. Adam has an endowment of 7 units of good 1 and 3 units of good 2 (i.e. wadam = (7, 3)), while Mark has an endowment of 3 units of good 1 and 7 units of good2 (wmark$ = (3,7)). The consumers' utility functions are given by: Uadam = Xa1 + Xa2 and Umark = min{xm1, Xm2) where x¡1 is the consumption of good 1 by consumer (i = adam, mark) (a) Find the set of Pareto optimal allocations of this economy (b) Find the Walrasian equilibrium.
In a two-good market, a consumer starts with an initial endowment of (x₁, x2) = (15.00, 5.00), while the market prices for these goods are given by (P1, P2) = (7.00, 3.00). The consumer has the following utility function: U 0.52 0.48 - Given this information, what will this consumer's final choice of quantity for each good be? x1 = x2 =
(1) Consider a small exchange economy with two consumers, A and B, and two commodities, ₁ and 2. Consumer A's initial endowment is 3 units of ₁ and 2 unit of 2. Consumer B's initial endowment has 5 units of 2₁ and 4 units of r2. Consumer A's utility function is given by U(₁, ₁) = x^x^. Consumer B's utility function is given by U(x,x) = 2x² + x2. Note that and are the amounts of the two goods for Consumer A, and rf and are amounts of the two goods for Consumer B. (a) Draw an Edgeworth box, showing the initial allocation. Label it as E. Measure Consumer A's consumption from the lower left and Consumer B's from the upper right. Also measure the number of ₁ on the horizontal axis and the number of r2 on the vertical axis. (b) Draw Consumer A's indifference curve (ICA) going through E. (c) Draw Consumer B's indifference curve (ICB) going through E.

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