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A swap economy has two consumers with spending functions: el(p, u) = (3(1.5)2pįp2e4)1/3 e2(p, u) =...
Consider an economy with two consumers A and B. Consumers A and B have utility functions...
Consider an economy with two consumers A and B. Consumers A and B have utility functions u(x+x)= Inx;" + Inx, and (x,x) - Inx' +-Inx, respectively. They face prices P, and P, for good 1 and good 2, respectively, and they have incomes “and I°, respectively a) Write formally the economic problem faced by consumer A and derive the demand functions xi (P1, P2,7") and x(P,P2,7^) [6] b) What are consumer B's demand functions for the two goods 1 and...
This Problem is from "Advanced Microeconomic Theory – Geoffrey Jehle, Philip Reny" 5.12 There are two...
This Problem is from "Advanced Microeconomic Theory – Geoffrey Jehle, Philip Reny" 5.12 There are two goods and two consumers. Preferences and endowments are described by u1(x1, x2) = min(x1, x2) and e1 = (30, 0), v2(p, y) = y/2 √ p1p2 and e2 = (0, 20), respectively. (a) Find a Walrasian equilibrium for this economy and its associated WEA. (b) Do the same when 1’s endowment is e1 = (5, 0) and 2’s remains e2 = (0, 20).
1. Consider the following exchange economy. There are two goods (1 and 2) and two consumers (A an...
1. Consider the following exchange economy. There are two goods (1 and 2) and two consumers (A and B). Preferences and endowments are as follows: uA (イ·攻)-玲攻 TA _ (0,2) 2(4,0) (a) Draw an Edgeworth Box diagram to depict this economy. Your diagram should be clearly labelled, and should include the autar kic allocation as well as a couple of indifference curves for each consumer. (Indifference curves for A do not need to be precisely accurate but those for B...
3. Consider a two consumer endowment economy. Consumer 1 and consumer 2 come into the economy...
3. Consider a two consumer endowment economy. Consumer 1 and consumer 2 come into the economy with an endowment of good x and good y. They can voluntarily trade their endowments. They have the following utility functions and endowments: u1(x,y) = zły: u2(z, 1) = a* * And they have the following endowments: Consumer 1 e1 = (4,12) Consumer 2 e2 = = (8,6) (a) Set up the utility maximization problem for consumer 2. Then solve for the demand functions...
13. (14pts) An exchange economy with two consumers (A and B) and two goods (1 and 2): Endowments wA= (2/3, 1/3) and...
13. (14pts) An exchange economy with two consumers (A and B) and two goods (1 and 2): Endowments wA= (2/3, 1/3) and w= (1/3, 2/3) Utility functions: u (xf,x4) = xfx4 and u(xf,x) = xfx 1 for normalization. Setting p1 Calculate the competitive equilibrium price, allocations, and utilities for each consumer 1) (2pts) Derive the contract curve and the core path (express x 2) as a function of xf). (2pts) 3) Suppose that we add the third consumer in this...
Consider an exchange economy with two consumers, A and B, who can consume only two goods....
Consider an exchange economy with two consumers, A and B, who can consume only two goods. Suppose consumers’ preferences are represented by a Cobb- Douglas utility function of the form u(x1i,x2i) = x1ix2i (here i is for consumer A or B) for a consumption bundle of two goods (x1i,x2i). The consumers have endowments eA = (e1A;e2A) = (4;1) and eB = (e1B;e2B) = (1;4). The price of good 1 is p1 and the price of good 2 is p2. You...
3. This question is adapted from our textbook. Anne and Bill live in an island economy...
3. This question is adapted from our textbook. Anne and Bill live in an island economy and consume only two goods. Let x? = (x1, xi) denote the consumption bundle for i = A, B. Their endowments are wa = (WA,WA) = (2,5) and wb = (wp,w?) = (10, a). Both have identical Cobb-Douglas utility functions ui(x) = xix, for i = A, B. Normalizing the price of good 2 to be p2 = 1, we just write pı =...
Consider the following economy of exchange. There are two goods and two consumers. The two goods...
Consider the following economy of exchange. There are two goods and two consumers. The two goods are called tillip and quillip and the two consumers are called 1 and 2. Consumer 1 has the utility function U1(t, q) = . 4ln(t)+ . 6ln(q) (where t is the amount of tillip and q is the amount of quillip). Consumer 2 has the utility function U2(t,q)=. 5ln(t)+. 5ln(q). Consumer 1 is equipped with 10units of quillip and tillip each. Consumer 2 is...
Consider a pure exchange economy with two consumers and two goods. Total endowments of the two...
Consider a pure exchange economy with two consumers and two goods. Total endowments of the two goods are given by X̅=10 and Y̅=20. Consumer A’s utility function is given by UA(XA,YA)=sqrtXAYA.. Consumer B regards the two goods as perfect substitutes with MRS=2. (1) Find the contract curve for this economy. (2) Suppose the initial endowments are given as the following: 2,8), (XA, YA)=(2,8) (XB,YB)=(8,12). Find the set of Pareto efficient allocations that Pareto dominate the endowment poin
Description of the economy: For each of the following problems, consider a 2x2 Exchange Economy with two consumers A and B, and two goods X and Y . The preferences of consumer A can be represented by...
Description of the economy: For each of the following problems, consider a 2x2 Exchange Economy with two consumers A and B, and two goods X and Y . The preferences of consumer A can be represented by the utility function uA(xA, yA) = xAyA , where xA is the amount of good A consumed by consumer A, and yA is the amount of good Y consumed by consumer A. The preferences of consumer B can be represented by the utility...
Consider an economy with two consumers A and B. Consumers A and B have utility functions u(x+x)= Inx;" + Inx, and (x,x) - Inx' +-Inx, respectively. They face prices P, and P, for good 1 and good 2, respectively, and they have incomes “and I°, respectively a) Write formally the economic problem faced by consumer A and derive the demand functions xi (P1, P2,7") and x(P,P2,7^) [6] b) What are consumer B's demand functions for the two goods 1 and...
1. Consider the following exchange economy. There are two goods (1 and 2) and two consumers (A and B). Preferences and endowments are as follows: uA (イ·攻)-玲攻 TA _ (0,2) 2(4,0) (a) Draw an Edgeworth Box diagram to depict this economy. Your diagram should be clearly labelled, and should include the autar kic allocation as well as a couple of indifference curves for each consumer. (Indifference curves for A do not need to be precisely accurate but those for B...
3. Consider a two consumer endowment economy. Consumer 1 and consumer 2 come into the economy with an endowment of good x and good y. They can voluntarily trade their endowments. They have the following utility functions and endowments: u1(x,y) = zły: u2(z, 1) = a* * And they have the following endowments: Consumer 1 e1 = (4,12) Consumer 2 e2 = = (8,6) (a) Set up the utility maximization problem for consumer 2. Then solve for the demand functions...
13. (14pts) An exchange economy with two consumers (A and B) and two goods (1 and 2): Endowments wA= (2/3, 1/3) and w= (1/3, 2/3) Utility functions: u (xf,x4) = xfx4 and u(xf,x) = xfx 1 for normalization. Setting p1 Calculate the competitive equilibrium price, allocations, and utilities for each consumer 1) (2pts) Derive the contract curve and the core path (express x 2) as a function of xf). (2pts) 3) Suppose that we add the third consumer in this...
3. This question is adapted from our textbook. Anne and Bill live in an island economy and consume only two goods. Let x? = (x1, xi) denote the consumption bundle for i = A, B. Their endowments are wa = (WA,WA) = (2,5) and wb = (wp,w?) = (10, a). Both have identical Cobb-Douglas utility functions ui(x) = xix, for i = A, B. Normalizing the price of good 2 to be p2 = 1, we just write pı =...
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