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(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 2₁ 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(r₁, ₁) = x₁x₁. Consumer B's utility function is given by U(x,x) = 2x³ + 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.

(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 2₁ 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(r₁, ₁) = x₁x₁. Consumer B's utility function is given by U(x,x) = 2x³ + 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.

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Please help, use second image as reference (different equation)

(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 2₁ 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(r₁, ₁) = x₁x₁. Consumer B's utility function is given by U(x,x) = 2x³ + 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 x2 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. (d) Is the initial endowment (E) Pareto-optimal? Explain your answer. (e) Draw the contract curve in the same Edgeworth box. 9 8 7 6 ان 4 3 2 1 0 012 3 4 5 6 7 8 9
Transcribed Image Text:(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 2₁ 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(r₁, ₁) = x₁x₁. Consumer B's utility function is given by U(x,x) = 2x³ + 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 x2 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. (d) Is the initial endowment (E) Pareto-optimal? Explain your answer. (e) Draw the contract curve in the same Edgeworth box. 9 8 7 6 ان 4 3 2 1 0 012 3 4 5 6 7 8 9
(1) Consider a small exchange economy with two consumers, Astrid and Birger, and two commodities, herring (H) and cheese (C). Astrid's initial endowment is 4 units of herring and 1 unit of cheese. Birger's initial endowment has 2 units of herring and 7 units of cheese. Astrid's utility function is given by U(II^,C)-I^C^. Birger is a more inflexible person. His utility function is given by U(HC) - min{HⓇ,C³}. Note that Hand C are the amounts of herring and cheese for Astrid, and HⓇ and Care amounts of herring and cheese for Birger. (a) Draw an Edgeworth box, showing the initial allocation. Label it as E. Measure Astrid's consumption from the lower left and Birger's from the upper right. Also measure the number of herring on the horizontal axis and the number of cheese on the vertical axis. See below. (b) Draw Astrid's indifference curve (ICA) going through E. Drawn in green, see below. Note that Astrid's initial utility is 4 (U(Hª, CA) – 4 × 1 – 4). Hence, we can trace his indifference curve by 4- HACA. On the graph, it is easier to see it by (e) Draw Birger's indifference curve (IC) going through E. Notice that Birger's indifference curve is L-shaped, and its corner of the L-shape is at H² = C. His endowment is at H³ = 2 and C8 = 7, which gives him utility of 2 units. Thus, the Indifference curve must have the corner at (2, 2) from O", see below. (d) Is the initial endowment (E) Pareto-optimal? Explain your answer. No, it is not Pareto optimal. Consider, for example, a trade that Astrid gives 1 unit of H to Birger and Birger gives 1 unit of C to Astrid. This trade is feasible and graphically, the allocation is at (3, 2) from Astrid's point of view (the north west of E). After this trade, Astrid will get the utility of 6 (A-3 x 2-6), which is higher than at E. For Birger, he will get the utility of 3, which is also higher than at E. So, this trade is feasible and make both better off than at E. Thus, E is not Pareto optimal. CA 9 7 6 5 4 3 2 1 you 1 2 3 4 D 5 6 OR TOA 7 9
Transcribed Image Text:(1) Consider a small exchange economy with two consumers, Astrid and Birger, and two commodities, herring (H) and cheese (C). Astrid's initial endowment is 4 units of herring and 1 unit of cheese. Birger's initial endowment has 2 units of herring and 7 units of cheese. Astrid's utility function is given by U(II^,C)-I^C^. Birger is a more inflexible person. His utility function is given by U(HC) - min{HⓇ,C³}. Note that Hand C are the amounts of herring and cheese for Astrid, and HⓇ and Care amounts of herring and cheese for Birger. (a) Draw an Edgeworth box, showing the initial allocation. Label it as E. Measure Astrid's consumption from the lower left and Birger's from the upper right. Also measure the number of herring on the horizontal axis and the number of cheese on the vertical axis. See below. (b) Draw Astrid's indifference curve (ICA) going through E. Drawn in green, see below. Note that Astrid's initial utility is 4 (U(Hª, CA) – 4 × 1 – 4). Hence, we can trace his indifference curve by 4- HACA. On the graph, it is easier to see it by (e) Draw Birger's indifference curve (IC) going through E. Notice that Birger's indifference curve is L-shaped, and its corner of the L-shape is at H² = C. His endowment is at H³ = 2 and C8 = 7, which gives him utility of 2 units. Thus, the Indifference curve must have the corner at (2, 2) from O", see below. (d) Is the initial endowment (E) Pareto-optimal? Explain your answer. No, it is not Pareto optimal. Consider, for example, a trade that Astrid gives 1 unit of H to Birger and Birger gives 1 unit of C to Astrid. This trade is feasible and graphically, the allocation is at (3, 2) from Astrid's point of view (the north west of E). After this trade, Astrid will get the utility of 6 (A-3 x 2-6), which is higher than at E. For Birger, he will get the utility of 3, which is also higher than at E. So, this trade is feasible and make both better off than at E. Thus, E is not Pareto optimal. CA 9 7 6 5 4 3 2 1 you 1 2 3 4 D 5 6 OR TOA 7 9
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