Consider an exchange economy with two agents, Aladdin and Belle: Aladdin and Belle each have an endowment of magic beans (good 1) and gold coins (good 2). . We'll fix the price of a gold coin at p2 = 1 for this entire problem. Aladdin has endowment (1. A) = (120, 240) and preferences u^(11, 12) = { In 21 + In 12. Belle has endowment (ep, c) = (60, 30) and preferences uB(21,22) = { In 21 + In 32. = (a) What is the formula for Aladdin's MRS? What is his MRS at his endowment point? (b) What is the formula for Belle's MRS? What is her MRS at her endowment point? (c) Describe the range of potential price ratios at which Aladdin and Belle might trade: that is, for what values of p will one choose to buy magic beans, and the other choose to sell them? Who will supply magic beans, and who will demand them? (d) Derive expressions for Aladdin and Belle's gross demands for magic beans, 2 (p1) and (P1). (e) Derive expressions for the net supply of magic beans, S.(p1) and the net demand for magic beans, D.(P1), within the price range you found in (c). (f) Suppose p = 2. How much will be supplied and demanded of magic beans? Is this above or below the equilibrium price? Explain. (g) Find the equilibrium price and quantity of magic beans. BRIEFLY explain how this price reflects both scarcity and preferences in this economy. (h) Plot the supply and demand curves for magic beans. On your graph, clearly indicate the vertical intercepts of the supply and demand curves, the equilibrium price and quantity, and the quantities demanded and supplied if p1 = 2. (i) In an Edgeworth Box diagram, precisely draw the initial allocation, the equilibrium allocation, and the equilibrium price line. Then sketch the indifference curves passing through the equilibrium allocation. 6) In an Edgeworth Box diagram, precisely draw the initial allocation, the price line corresponding to pi = 2, the allocation Aladdin would select if p = 2, and the allocation Belle would select if pi = 2. Then sketch the indifference curves passing through those two points. (k) In an Edgeworth Box diagram, sketch the contract curve for this situation. (It need not be mathematically precise, but should have the right shape.) Explain why the the contract curve is located where it is, relative to a diagonal line connecting the two origins. (Is it the same as the line? Always go above it or below it? How is this related to Aladdin and Belle's endowments and/or preferences?) Consider an exchange economy with two agents, Aladdin and Belle: Aladdin and Belle each have an endowment of magic beans (good 1) and gold coins (good 2). . We'll fix the price of a gold coin at p2 = 1 for this entire problem. Aladdin has endowment (1. A) = (120, 240) and preferences u^(11, 12) = { In 21 + In 12. Belle has endowment (ep, c) = (60, 30) and preferences uB(21,22) = { In 21 + In 32. = (a) What is the formula for Aladdin's MRS? What is his MRS at his endowment point? (b) What is the formula for Belle's MRS? What is her MRS at her endowment point? (c) Describe the range of potential price ratios at which Aladdin and Belle might trade: that is, for what values of p will one choose to buy magic beans, and the other choose to sell them? Who will supply magic beans, and who will demand them? (d) Derive expressions for Aladdin and Belle's gross demands for magic beans, 2 (p1) and (P1). (e) Derive expressions for the net supply of magic beans, S.(p1) and the net demand for magic beans, D.(P1), within the price range you found in (c). (f) Suppose p = 2. How much will be supplied and demanded of magic beans? Is this above or below the equilibrium price? Explain. (g) Find the equilibrium price and quantity of magic beans. BRIEFLY explain how this price reflects both scarcity and preferences in this economy. (h) Plot the supply and demand curves for magic beans. On your graph, clearly indicate the vertical intercepts of the supply and demand curves, the equilibrium price and quantity, and the quantities demanded and supplied if p1 = 2. (i) In an Edgeworth Box diagram, precisely draw the initial allocation, the equilibrium allocation, and the equilibrium price line. Then sketch the indifference curves passing through the equilibrium allocation. 6) In an Edgeworth Box diagram, precisely draw the initial allocation, the price line corresponding to pi = 2, the allocation Aladdin would select if p = 2, and the allocation Belle would select if pi = 2. Then sketch the indifference curves passing through those two points. (k) In an Edgeworth Box diagram, sketch the contract curve for this situation. (It need not be mathematically precise, but should have the right shape.) Explain why the the contract curve is located where it is, relative to a diagonal line connecting the two origins. (Is it the same as the line? Always go above it or below it? How is this related to Aladdin and Belle's endowments and/or preferences?)
