Consider an Edgeworth box economy where preferences are given by u²(x,x)=x+Inx and u²(x,x)=xx. and the initial endowments are e¹=(1,3) and e²=(3, 1). Find all the Walrasian equilibrium. You may assume that the solution is inte- rior.
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- 6. Consider an Edgeworth box economy where preferences are given by u'tri.) = 2/x} + x and utui,) = 2/ +3, (a) Suppose the initial endowments are e' = (4,4) and e = (1,1). Find all the Pareto optimal allocations. (b) Find the Walrasian equilibrium.Consider a pure-exchange general equilibrium model with two consumers, two goods and an initial endowment. Assuming that consumers have convex preferences, a Pareto improvement can be achieved through exchange: a. As long as indifference curves associated with the endowment are tangent to each other on the Edgeworth box. b. As long as indifference curves associated with the endowment are not tangent to each other on the Edgeworth box. с. Only when one of the consumers has no endowment of one of the goods. d. Only when the initial endowment is on the contract curve.Sarah and Andrew are two traders in a pure exchange economic with two goods, Bikes (B) and Computers (C). Sarah's preferences are described by the Cobb-Douglas Utility function: U, = B!³ C?3 1/3 S. Andrew's preferences are given by: UA = B}{²C}2 ´A Assume the price of Bikes is 1 and the price of computers is p. The initial endowments are BA = 10, Bs = 20, CA = 20 and Cs= 10. What is the equilibrium price of computers relative to bikes (p)? %3D %D
- Ashly and Betty consume X and Y. Ashly’s utility function is UA=XA0.6YA0.4 Betty's utility function is UB= XB0.4YB0.6 Their inital endowments are XA=10 , YA= 20, XB=20, YB= 10 Assuming that the price of Y is equal to 1, compute the competitive equilibrium of this economy (i.e. the price of X at which demand for X equals supply of X and demand for Y equals supply of Y).Adam's utility function is U^(r.y) = = (12,12). Bob's utility funetion is U"(r. u) = 2r+3y and his initial endowmen is w= (12, 12). Find the Walrasian equilibrium allocation [(r, y^), (r", y")) ane min{3r, 2y} and his initial endowment price ratio px/Py for this exchange economy. Type your answer here:Consider a 2-good, 2-agent pure exchange economy with complete markets (no externalities) and let the initial endowment be еA = (10, 10), eg = (20, 10). Which 2 of the following 8 options are false: At prices p = (1, 1) both agents' budget sets are subsets of the Edgeworth box. If preferences are represented by UA, UB: R³0 21 3. →R where UA (XA) = XA1 XA2 and us (XB) = x₁x2 then the initial endowment is Pareto efficient. If Andy has strongly monotonic preferences then the bottom left corner of the Edgeworth box, OA, is Pareto efficient. The Edgeworth box is 30 units wide and 20 units high. If in Walrasian Equilibrium players trade to XA = (14, 8), XB = (16, 12) then Walrasian Equilibrium prices must be p = (1, 2). If Andy has strongly monotonic preferences then the top right hand corner of the Edgeworth box, Og, is Pareto efficient. If Andy has strongly monotonic preferences then it is impossible to have a Walrasian Equilibrium where one of the prices equals 0. If preferences are…
- Competitive general equilibrium Amy(A) and Brian (B) have the following utility function U^A= 2XaYa, U^B= √XbYb Were there endowment of consumption good X and Y are as follows: Xa= 60 Ya = 80 Xd=30 Yb=180 At the endowment point what is the marginal rate of substitution of X for Y for Amy? For Brian? Find the competitive equilibrium price of the goods at which the consumers trade with each other In the competitive equilibrium for each unit of good Y how many units of good X can be exchanged. Find both brian and amy preferred consumption bundles in the equilibrium Is the allocation of resources achieved in part d pareto-optimal? Explain. Draw the edgeworth box that shows all possible allocations and plot the endowment points. Plot the indifferent curves of the two consumers and the contract curve in the edgeworth box as well.Consider a 2-good, 2-agent pure exchange economy where there are 10 units of each good and preferences are represented by UA, UB: RR where uA (XA) = 2XA1 + XA2 and uB (XB) = XB1 + 2XB2- Which 2 of the following 8 options are true: There are initial endowments from which we can have a Walrasian Equilibrium with prices p = (1, 0). O The only Pareto efficient allocation is XA = (10, 0), XB = (0, 10). Every Pareto efficient allocation can be supported as a Walrasian Equilibrium after some reallocation of resources. We cannot apply the First Welfare Theorem because preferences violate local non-satiation. The allocation XA = (5, 10), XB = (5, 0) is Pareto efficient. For all price vectors PER3 we have p1z₁ + P2z2 = 0 where z; is the excess demand of good i € {1, 2}. O Preferences of both players satisfy strict convexity. At initial endowment eA= (5, 5), eg = (5, 5), there is a Walrasian Equilibrium with prices p = (1, 2).John and Belle consume only two goods, x and y. They have strictly convex preferences and no kinks in their indifference curves. At the initial endowment point, the ratio of John's marginal utility of x to his marginal utility of y is J and the ratio of Belle's marginal utility of x to her marginal utility of y is B, where ] B. b. C < J. c. C = J. d. C = B. e. Jd) An exchange economy has two goods (apples, bananas) and two types of agents (1, 2). Endowment of agent 1 is (3 bananas, 3 apples), and endowment of agent 2 is (4 bananas, 2 apples). Both goods are divisible goods, so that it is possible to consume frac- tions of each good (e.g. 4.92 bananas and apples). Each type 1 agent's preferences are represented by the utility function U(x,x) = min{x, x}, where x and x denote the agent's consumption of bananas and apples, respectively. Each type 2 agent's preferences are represented by the utility function U(x3, x²) = 7min{x3, x4} where x and r² denote the agent's consumption of bananas and apples, respectively. Use an Edgeworth's Box to depict the set of Pareto efficient allocations in this economy. Please capture consumption of bananas on the horizontal axis.In an exchange economy, two agents have utility functions u^(x, y) = x2 y and u"(x, y) = x · y, respectively, from x units of Good 1 and y units of Good 2. Assume the initial endowments are w A = (@A.1,2) and oB = (32,40), respectively. Suppose that an equilibrium is found in which the prices of the good are equal (that is, Pi = P2, i.e., the relative price is 1). If WA.1 = 60, then wA.2 %3DPlease answer all parts it would mean alot. For the rest of this question consider a two goods economy where Kim and Jung can trade Ferraris (good x) and VR headsets (good y) with each other. Kim and Jung both enjoy driving Ferraris and having more VR headsets (so more friends can play the same game). They start at the same (high) level of income. Kim has an initial endowment of (x0k, y0k) = (10,30) and Jung has an initial endowment of (x0j, y0j) = (30,10) a) Illustrate the initial endowment in an Edgeworth box. Clearly label the axes and explain the dimensions of the box. Show the indifference curve each of them is on at the endowment point. b) Consider an allocation where Kim gets (xk, yk) = (40,40) and Jung gets the remaining Ferraris and VR headsets. Show where this point is in the Edgeworth box. Is this allocation Pareto efficient? Is it equitable? How likely is this to arise in practice? c) Assume that Kim has preferences Uk (Xk, Yk) = 3Xk + 3Yk and Jung has…SEE MORE QUESTIONS