Consider an exchange economy with two consumers, A and B, whose utilities are given as above. How- ever, the parameter d is lower for consumer A than for consumer B, i.e., we have ª ≤ 6³. Consumer A is endowed with 2 units of good 1, but has no endowment of good 2. Consumer B has no endowment of good 1, but has 2 units of good 2. In the remainder of this question, let p denote the price of good 1 and the price of good 2 be normalised to 1. (ii) Find the competitive equilibrium price p and the equilibrium allocation expressed as a function of the parameters 84 and 6B. Who is consuming more of good 1 and who consumes more of good 2? Interpret your results by referring to your answer in part (i).
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- Please answer every part. 4. Consider an economy consisting of two individuals, Ann and Bob, and two goods, scotch and wine. Aun has 5 bottles of scoteh and 2 bottles of wine as her endowment, while Bob has 3 bottles of each. Suppose their preferences are described by the following utility functions uA(s, w) = sw and up(s, w) = s'u. Assume also that the prices of goods scotch and wine are represented by P,= 1 (scotch is the mumeraire), and P>0. a. Sketch the Edgeworth box of the economy with Ann at the lower left corner and Bob at the upper right corner; scotch on the horizontal axis, and wine on the vertical axis. Indicate the endowment point e in the box. b. Write the budget lines for Ann and Bob. e. Solve Ann's utility maximization problem. Expross Ann's optimal consumption bundle in terms of P. d. Solve Bob's utility maximization problem. Express Bob's optimal consumption bundle in terms of P. e. Define competitive equilibrium. Compute and plot the CE for this problem.5. Sheila and Bruce are taking a canoe trip. Sheila brought 10 boxes of peanuts (x) and 15 bags of chips (y). Sheila's utility function is U*(x,y) = lnvx*+ Invy°. Bruce also brought 20 boxes of peanuts and 5 bags of chips. Bruce's utility function is UB(x.y) = min[x', y'I. a) Illustrate the endowment point and draw a sample set of indifference curves through the endowment point. b) If Sheila and Bruce trade what will be the pattern of mutually beneficial trade? c) If the terms of trade are the number of bags of chips (y) per box of peanuts (x) then what is the largest value that these terms can be for a mutually beneficial trade in this economy? d) Find one mutually beneficial trade where the terms of trade are 1 bag of chips (y) per 2 boxes of peanuts (x). Suppose that Sheila and Bruce set up two competitive markets for peanuts and chips. Below you will show that if the price of peanuts (x) is $1 and the price of chips (y) is $2 then the markets for both peanuts and chips will clear.…2) Two consumers R and S share an endowment (x, y) of goods X and Y. The consumers' utilities from consumption can be written as UR = aln(XR) + bln(YR), and Us=aln(xs) + bln(ys), where XR, XS, YR, and ys are the quantities which each consumes, and a and b are parameters, for which a + b =1. Write a report in which you a) Define the concept of the contract curve, and show that for these endowments, it will be the upward diagonal of the Edgeworth box, which shows all possible divisions of the endowment. b) Assume that in the initial endowment, XRE = XE and ysE=yE. R begins with the endowment of X and S begins with the endowment of Y. By setting up a constrained maximisation problem for each consumer, obtain their offer curves, and hence obtain the Walrasian equilibrium. c) State the two welfare theorems, and explain how they apply in this case.
- Let the following table represents the total utility of a given consumer, in the cardinal utility approach. Q 1 2 3 4 5 6 7 TUX 8 14 18 20 20 18 16 TUY 6 10 13 15 16 16 14 MUX MUY MUX/PX MUY/PY Calculate the MUX and MUY and fill the table in the 4th and 5th rows. If the two products (X&Y) are free goods how many of X and Y should the consumer take to maximize utility? What is the maximum utility of X and Y if they are free? Let now price of X is 4 birr per unit and price of Y is 2 birr per unit. Calculate MUX/PX and MUY/PY and fill the 6th and 7th row. Assuming the consumer has any amount of money (enough budget) how many of X and Y should the consumer buy, to maximize utility? What is the total utility of X and Y? Let now price of X is 4 birr per unit and price of Y is 2 birr per unit and budget of the consumer for consumption of X and Y is 20 birr. Given budget constraint how many of X and Y should the consumer buy to maximize utility?2. Assuming Bart and Homer barter (no pun intended), highlight the area of all post-trade allocations both of them prefer to their initial endowment. 3. What determines which particular post-trade allocation they end up with? Marge observes what is going on and intervenes. She (acting as the "Government' in our example) decides that Bart should not have any beer. She makes a lump-sum transfer leading to new initial endowments for Bart (0,21) and Homer (38,0). 4. In your Edgeworth box show the new initial endowments after the lumpsum transfer imposed by Marge. Label this poișt e2. (1 point) 5. After Marge's transfer mark one new possible post-trade allocation (Label this point f.) and draw the associated indifference curves for Bart and Homer. (1 point) 6. Did Marge succeed in her mission to not let Bart have any beer? Why or why not? 7. Add the contract curve to your Edgeworth box. 8. What do all points on the contract curve have in common?3. Christina loves pizza and hates burger. Her utility function is U(p – b) = p – 6", where is the number of pizzas she consumes and b is the number of burgers she consumes. John likes both pizza and burger. His utility function is U(p, b) = p + 2\b Christina has an initial endowment of no pizzas and 8 burgers. John has an initial endowment of 16 pizzas and 8 burgers. a. Graph the initial endowment and label it E b. If Christina hates burgers and John likes them, how many burgers can Christina and John be consuming at a Pareto optimal allocation? What is John's marginal utility for pizzas and burgers? Mark the locus of Pareto optimal allocations of pizzas and burgers between Christina and John on the grapsh above.
- 7) Jane has 3 liters of soft drinks and 9 sandwiches. Bob, on the other hand, has 8 liters of soft drinks and 4 sandwiches. With these endowments, Jane's marginal rate of substitution ( MRS) of soft drinks for sandwiches is 4 and Bob's MRS is equal to 2. Draw an Edgeworth box diagram to show whether this allocation of resources is efficient. If it is, explain why. If it is not, what exchanges will make both parties better off?True/false, no need to explain. (a) There is no perfect way to aggregate individual preferences to a single "social" preferences (b) “Before enacting a policy, try to put ourself in the shoes of those who will be negatively impacted mostly.” This sentence is best to summarise the Benthamite welfare function (c) If a person's utility is simply a function of her own consumption, and the welfare function is derived from individuals utility function, then we will not have consumption externalities. (d) An allocation cannot be both equitable and Pareto efficient.Can you help me with this question. Im finding it quite difficult. In a two-good economy there are two equal-sized groups of people: type a have preferences given by 2 log(xa1) + log(xa2) and type b have preferenceslog(xb1)+2log(xb2) where xhi means consumption by a type h person of good i. The division of property is as follows: each a-person has an endowment of (30, k) units of the two goods; each b-person has an endowment of (60, 210−k) units, where k is some given number between 0 and 210. Assume that there is no production and that people can freely exchange goods to maximise their utility. If there is a competitive equilibrium, what are the individuals’ incomes (ya, yb) in equilibrium as a function of k?
- Neha and Sonam consume only Coke and Pepsi in a two person and two goods exchange economy. Neha consumes these two goods in fixed proportions such that she consumes 2 bottles of coke with 1 bottle of Pepsi. Sonam's utility function is given by U = 4P + 3C . In the economy, there is a total of 100 bottles of Pepsi and 200 bottles of Coke. If Neha initially had 60 bottles of Pepsi and 80 bottles of coke, then in the equilibrium position, Sonam will consume: A. between 50 to 60 bottles of Pepsi B. between 52 to 60 bottles of Pepsi C. between 54 to 60 bottles of Pepsi D. between 56 to 60 bottles of PepsiQuestion 6: Transitivity There is only one consumption good in the world (cities). Karen is moving – suppose that her preferencesover cities are described as follows: she strictly prefers city A to city B if either (1) the average rent in cityA is cheaper than in city B, or (2) the average rent is the same in both cities, and there are more goodrestaurants in city A than in city B. Are these preferences transitive? Justify your answer.ote: - You are attempting cuestios suro 12 Neha and Sonam consume only Coke and Pepsi in a two person and two goods exchange economy. Neha consumes these two goods in fixed proportions such that she consumes 2 bottles of coke with 1 bottle of Pepsi. Sonam's utility function is given by U=4P+BC. In the economy, there is a total of 100 bottles of Pepsi and 200 bottles of Coke. If Neha initially had 60 bottles of Pepsi and 80 bottles of coke, then in the equilibrium position, Sonam will consume: A. between 50 to 60 bottles of Pepsi B. between 52 to 60 bottles of Pepsi C. between 54 to 60 bottles of Pepsi D. between 56 to 60 bottles of Pepsi Answer 04:09 PM 19-10-2021