Jack Sparrow's utility function is UJack(W, B) = W. His wife's utility function is Uwife(W, B) = B. Jack endowment is 17 bottles of wine and 5 books and Jack's wife's endowment is 20 bottles of wine 14 books. In the Edgeworth box, Jack's consumption is measured from the lower left corner, and his wife's the upper right corner of the box; the wine is on the horizontal axis and books are on the vertica axis. Therefore, in an Edgeworth box for Jack and his wife, there is only one Pareto Optimal allocation that is located in the top left corner of the box. True or False? Please submit 1 if True and O if False.
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- A and B consume only two goods, cider (C) and dumplings (D). A has an initial endowment of 10 bottles of C and 30 of D. Bob has an initial endowment of 50 bottles of cider and 50 dumplings. Alice’s utility function is uA(CA,DA) = 9ln(CA) + 10ln(DA), where CA and DA represent consumption of C and D, respectively. B’s utility function is uB(CB,DB) = CBXDB, where CB and DB denote B's consumption of C and D. a) Find the competitive equilibrium, i.e. the price ratio, of this exchange economy and the resulting equilibrium allocation. b) Find the expression of the contract curve for this economy and use your answer to check that the equilibrium allocation you found in (b) is indeed Pareto optimal.Refer to figure. Suppose the consumer is endowed with 10 units of orange and consumes 5 units of apple. The price of the apple decreases and at the new price the consumer consumes 9 units of apple. The change in the demand for apples due to the endowment effect is equal to_____Consider a hypothetical consumer named Hayden who is shopping for bread and brie. The graph with bread and brie on the axes presents the utility‑maximizing combinations of bread and brie that Hayden chooses when the price of bread is $1.00$1.00 per loaf and the price of brie is $4.00$4.00 and $6.00$6.00 per wheel, respectively. The other graph shows Hayden's demand curve for brie. The two points and associated values in the graph for bread and brie combinations correspond to points A and B in the graph of the demand curve for brie. What are the specific prices and quantities of brie associated with points A and B on Hayden's demand curve? price of brie at point A: $$ quantity demanded at point A: price of brie at point B: $$ quantity demanded at point B:
- The following table shows the marginal utility per dollar of apples and pears for five consumers: Consumer Marginal Utility Per Dollar Apples Pears Darnell 8 5 Eleanor 7 8 Jacques 6 6 Kyoko 5 4.5 Musashi 4 4 Darnell, Eleanor, and Kyoko are not optimizing over their choice of fruit. In the following table, indicate which fruit each consumer should increase consumption of in order to achieve the optimal fruit consumption bundle. Consumer Apples Pears Darnell Eleanor KyokoRefer to figure. Suppose the consumer is endowed with 10 units of orange and consumes 5 units of apple. The price of the apple decreases and at the new price the consumer consumes 9 units of apple. The change in the demand for apples due to the endowment effect is equal to Optionsa) 3b) 4c) 1d) none of theseUse the Fundamental Theorem of Exchange and draw Edgeworth Box diagrams to show the conditions necessary for an 'efficient' allocation of two goods between two individuals. Use this model to evaluate the statement: "If two individuals have identical endowments of both goods there are no possible gains from trade". Hint: you need to develop your explanation of the theory and the efficiencyconditions step-by-step. You need to draw several diagrams showing Edgeworth Box
- Suppose that consumer I has the utility function u(x,y) = x + 2y and consumer II has the utility function u(x,y) = min{x, 2y}. Consumer I initially has 12 units of y and zero units of x, while consumer II has 12 units of x and zero units of y. It is correct to state that, in competitive equilibrium, the agents' consumption basket will be:Reese thinks peanut butter and chocolate are great when separate, but when they combine they are even more epic. In other words, Reese likes to eat either peanut butter or chocolate, but when he eats them together, he gets additional satisfaction from the combination. His preference over peanut butter (x) and chocolate (y) is represented by the utility function: u(x, y) = xy + x + y Suppose that now Reese loses almost his entire income, so that he is left with only one dollar, i.e. his new income is I0 = 1. If prices are still px = 2, py = 4, what is his new optimal consumption of x and y (Hint: Remember that consumption of both goods must be weakly positive, i.e. x∗ ≥ 0 and y∗ ≥ 0) (a) x∗ = 0.5, y∗ = 0(b) x∗ = 0.25, y∗ = 0(c) x∗ = 0.75, y∗ = 0.25(d) x∗ = 0.75, y∗ = 0(e) x∗ = 0.5, y∗ = 1Bob enjoys cookies (x) according to the utility function U(x)=20x- 2 tx , where t is a parameter that reflects how hungry he is. Cookies are costless in Bob’s world and so there is no income constraint. Using the envelope theorem, calculate how Bob’s maximum utility from eating cookies varies with t.
- For the rest of this question consider a two goods economy where Kim and Jung can trade Ferraris (good x) and VR headsets (good y) with each other. Kim and Jung both enjoy driving Ferraris and having more VR headsets (so more friends can play the same game). They start at the same (high) level of income. Kim has an initial endowment of (x0k, y0k) = (10,30) and Jung has an initial endowment of (x0j, y0j) = (30,10) c) Assume that Kim has preferences Uk (Xk, Yk) = 3Xk + 3Yk and Jung has preferences Uj (Xj, Yj) = Xj + 3Yj. Will Kim and Jung trade? Calculate the general equilibrium allocation for Kim and Jung. Compute the utility at the endowment point and at the general equilibrium allocation. Is the new allocation on the contract curve?Two students go out to lunch and decide to split the bill evenly between them. Each student has a quasi-linear utility function given by ui(fi , xi) = φi(fi) + xi , where φi(·) is strictly concave, fi is the amount of food consumed by student i, and xi is a composite numeraire good. Each student has a fixed budget of mi . EVALUATE THIS CLAIM: Both students eat too much!Jane has 11 liters of soft drinks and 10 sandwiches. Bob, on the other hand, has 9 liters of soft drinks and 10 sandwiches. With these endowments, Jane's marginal rate of substitution (MRS) of soft drinks for sandwiches is 6 and Bob's MRS is equal to 8. Draw an Edgeworth box diagram to show whether this allocation of resources is efficient. If it is explain why. If it is not, what changes will make both parties better off? Part 2 1.) Using the three-point curved line drawing tool, draw an indifference curve for Jane when consuming 11 liters of soft drinks and 10 sandwiches. Label this curve UJ. 2.) Using the three-point curved line drawing tool, draw an indifference curve for Bob when consuming 9 liters of soft drinks and 10 sandwiches. Label this curve UB.