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 and₂. Consumer A's initial endowment is 3 units of 2₁ and 2 unit of 2. Consumer B's initialendowment has 5 units of 2₁ and 4 units of r2. Consumer A's utility function is given byU(r₁, ₁) = x₁x₁.Consumer B's utility function is given byU(x,x) = 2x³ + x².Note that and are the amounts of the two goods for Consumer A, and rf and areamounts of the two goods for Consumer B.(a) Draw an Edgeworth box, showing the initial allocation. Label it as E. Measure Consumer A'sconsumption from the lower left and Consumer B's from the upper right. Also measure thenumber 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.9876ان43210012 3 4567 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 isgiven byU(II^,C)-I^C^.Birger is a more inflexible person. His utility function is given byU(HC) - min{HⓇ,C³}.Note that Hand C are the amounts of herring and cheese for Astrid, and HⓇ and Careamounts of herring and cheese for Birger.(a) Draw an Edgeworth box, showing the initial allocation. Label it as E. Measure Astrid'sconsumption from the lower left and Birger's from the upper right. Also measure the numberof 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 itby(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, theIndifference 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 Hto Birger and Birger gives 1 unit of C to Astrid. This trade is feasible and graphically, theallocation 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, hewill get the utility of 3, which is also higher than at E. So, this trade is feasible and makeboth better off than at E. Thus, E is not Pareto optimal.CA97654321you1234D56ORTOA79

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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.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter13: General Equilibrium And Welfare

Section: Chapter Questions

Problem 13.5P

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