Consider a pure exchange economy, where both consumers have exactly the same preferences, described by a Cobb-Douglas utility function, but have different endowments. In such an economy, an equitable distribution of goods (where each individual consumes exactly half of each good) is a Walrasian equilibrium allocatior v[ Select ] always, for any initial endowment.
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- Consider a pure exchange economy, where each consumer has preferences described by a Cobb-Douglas utility function. Both consumers have exactly the same endowment. In such an economy, an equitable distribution of goods (where each individual consumes exactly half of each good) is a Walrasian equilibrium allocation. a. always for any consumers' preferences b.only if consumers' preferences are exactly the same c. never d. non of the aboveConsider a pure exchange economy, where each consumer has preferences described by a Cobb-Douglas utility function. Both consumers have exactly the same endowment. In such an economy, an equitable distribution of goods (where each individual consumes exactly half of each good) is a Walrasian equilibrium allocation? a. always, for any consumers' preferences b. only if consumers' preferences are exactly the same c. Never d. None of the aboveAssume that there is two-person two-commodity pure exchange economy. A's utility function is u^ (x,x) = x + ln x2 and his endowment is w4 = (1,4). B's utility function is u²(x,x) = x + 2 In x2 and his endowment is w = (3,2). (a) Determine and draw the set of Pareto efficient allocations in an Edgeworth box for this economy (b) The price p₂ is normalized to 1; for simplicity we write p, as just p. Calculate the Walras equilibrium pricep and Walras allocation [(4,2), (2)]. Check that the Walras allocation is Pareto efficient graphically and algebraically.
- 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).Assume the setting outlined in Question 1. Suppose that the social planner considers it to be imperative that agent B consumes exactly one unit of good 1l and four units of good 2. Although the social planner can not force the individuals to a particular consumption, they can enforce transfers of good 1 between the consumers (transfers of good 2 are not enforceable by the social planner). What transfer of good 1 would guarantee that in the resulting competitive Walrasian equilibrium consumer B consumes one unit of good 1 and four units of good 2? Select 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 = in the corresponding competitive equilibrium. Therefore, no such transfers exist. 1 and æ = 4 O c. 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.A small exchange economy is comprised of two of individuals, A and B, and two types of goods, x, ,x,. The individuals' preferences over two goods are can be represented by the following utility functions: U*(x;,.x; ) = min (2.x,x; ) and U* (x;,x;) = min(x;.2x, ). Initial endowments are 10 x, (individual A), and 10 x, (individual B). Calculate the price ratio which yields an equilibrium in the exchange market.
- 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 %3DSarah 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 %DConsider a 2-good, 2-agent pure exchange economy where the initial endowment is eд = (5, 5), eß = (5, 5) and preferences are represented by UA, UB: R → R where UA (XA) UB (XB) = X₁X2 and Which 2 of the following 8 options are false: For all B [0, 1], the initial endowment is a Walrasian Equilibrium allocation. If B<1 then at prices p = (1,1) there will be excess demand of good 2 and excess supply of good 1. O For all B € [0, 1], every Pareto efficient allocation can be supported as a Walrasian Equilibrium for some reallocation of resources. O For any prices p = (1, 1), the budget sets of both players leave the Edgeworth box. For all B € [0, 1], the bottom left and top right corners of the Edgeworth box (0A and Og) are both Pareto efficient. For all B [0, 1], the Walrasian Equilibrium will be Pareto efficient. For all 8 [0, 1], Bob's preferences are strictly convex. For ß = 1/2, the Pareto Set is the straight line joining OA and Og.
- Consider a two-people, two-goods exchange economy, where Person A and Person B have the following utility functions. In which case, the Pareto optimal allocation can be on the boundary of the Edgeworth box? Note: Do not consider the origins as the boundary points. (Boundary points are the edges of the Edgeworth box except for the origins.) 0 UA = min (XA1, XA2) and Ug = Xg1.Xg2 (i) UA = log(xA1) + log(Xa2) and ug = 3Xgt + X82 (ii) uA = (XA1) 0XA) and ug = 3log(Xgy) + X82 %3! (iv) uA = (XA1)2 + XA2 and ug = log(xa1) + Xe2Consider a two-person, two good pure exchange economy. A's preferences over consumption bundles (x₁, x₂) are represented by the utility function UA (X₁, X₂) = x₁Xz B's preferences over consumption bundles are represented by the utility function UB (X₁, X₂) = x₁ + 2x₂ The initial endowment in goods x, and x₂ are given as: Individual A's as e^ = (1,0.5) and Individual B's as eB= (1, 1.5) 1. Draw an Edgeworth box indicating the endowment and preferences of this problem. 2. Find the set of Pareto Optimal Allocations in this economy and depict these in the Edgeworth box. MRSA = JUA/ƏX₁ X2 aUA/aX₂ X1 ƏUB/0x₁ MRSB = = 2 aUB/0x₂ Therefore, the set of all points where the MRS are equal are given by = 2 → X₂ = 2x1 Show Transcribed Text Advanced Microeconomics. Solve step by step so that I grasp the concept4) Consider a pure exchange economy with two goods, (x, y), and two consumers, (1, 2). Consumers' endowments are e1 = (4, 2) and e? = (6, 6) And their preferences are represented by utility functions: u(x, y) = x³y and u(x,y) = x³y$ (d) Set up the utility maximization problem for each consumer and solve for their Marshallian demand functions. (e) Compute the market demand for each good. () State the Walrus law for this economy and explain its economic interpretation. (g) Assume the excess demand for good x is zero, i.e., EDx = 0, and calculate the ratio of prices, i.e., p Ipy . Then, use this ratio of prices to show that the excess demand for good Yis also zero, i.e., EDy= 0. Briefly explain how this relates to the Walrus' law. (h) Given the price ratio found above, calculate the equilibrium allocations and show that feasibility, individual rationality, and Pareto efficiency holds.