Derive a co A A 5. Consider a two-consumer economy in which wA = (1,2), wB=(2, 2), u^(x₁, x2) = x₁³x2 B B and u²(x,x) = x, ³x₂5 (a) Illustrate this economy in an Edgeworth box. (b) Derive a competitive equilibrium for this economy. 1/J
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- Q3Use a matrix method to find the equilibrium prices and quantities where the supply and demand functionsfor Good 1, Good 2 and Good 3 are asQd1 = 50 − 2P1 + 5P2 − 3P3, Qs1 = 8P1 − 5Qd2 = 22 + 7P1 − 2P2 + 5P3, Qs2 = 12P2 − 5Qd3 = 17 + P1 + 5P2 − 3P3, Qs3 = 4P3 − 1Answer the questions based on the model given in the image: a. What is the set of Pareto optimal outcomes in this economy? Justify your answer. b. What is the competitive equilibrium in this economy assuming price of good 1 is set to 1. Specify whether the competitive equilibrium is pareto optimal. c. Now consider another economy where everything is as before, apart from individual 2’s preferences, which are as follows: among any two any bundles consisting of X and Y, individual 2 prefers the bundle which has a larger amount of commodity X irrespectiveof the amount of commodity Y in the two bundles, and between any two bundles with the same amount of X, she prefers the one with a larger amount of Y. (not sure but these are perhaps lexicographic preferences) Find the set of Pareto optimal outcomes in this economy.Consider two substitute products; movies and Box Office rentals. With the aid of graphical illustrations, explain why the outcome of a general equilibrium analysis can differ substantially from that of a partial equilibrium analysis, when evaluating the impact of a unit tax on movie tickets.
- Using general equilibrium analysis, and taking into account feedback effects, analyze the effects of increased taxes on airline tickets on travel to major tourist destinations such as Florida and California and on the hotel rooms in those destinations.Consider a two-good exchange economy with two types of consumers. Type A have the utility function And an endowment of 3 units of good 1 and k units of good 2. Type B has the utility function And an endowment of 6 units of good 1 and 21 - k units of good 2. a. Find the competitive equilibrium outcome and show that the equilibrium price p* = p1/p2 of good 1 in terms of good 2 is p* = 21+k/15. b. Find the income levels (MA; MB) of both types in equilibrium as a function of k. c. Suppose that the government can make a lump-sum transfer of good 2, but it is impossible to transfer good 1. Use your answer to part b to describe the set of income distributions attainable through such transfers. Draw this in a diagram. d. Suppose that the government can affect the initial distribution of resources by varying k. Find the optimal distribution of income if (i) the SWF is W = log(MA) + log(MB) and (ii) W = MA + MB.the demand and supply of two goods are given below Good1 demand: Q1=100-2P1+2P2 Good1 supply : Q1=2P1 Good2 demand : Q2=200-4P2+2P1 Good supply : Q2=20+2P2 based on the two demand equations , we can say that the goods are ________(complements,subsitutes,unrelated) These two markets are in equilibrium when P1= $_______ and P2=$_______ if the demand for the good 1 increases by 20 both prices will change even through only the demand for good 1 initially changes. the new general equilibrium will be P1=$_______________ P2=$_______________
- Which is the correct answer ? Suppose there are 10 apples and 10 oranges in the economy. Joe is currently consuming 4 apples and 5 oranges, and Jane is consuming 6 apples and 5 oranges. At this allocation, Joe's marginal utility of apples is 3, and his marginal utility of oranges is 5. Jane's marginal utility of apples is 6, and her marginal utility of oranges is 10. The current price of apples is R4 per unit and the current price of oranges is R5 per unit. To reach a competitive equilibrium, the required price adjustment is: A. A decrease in the orange price relative to the apple price. B. A decrease in the apple price relative to the orange price. C. No change in the relative prices. D. An increase in both prices.Q1 Consider the market for orange juice. In this market, the supply curve is given by QS = 100PJ −20PO and the demand curve is given by QD = 1000−150PJ +100PC, where J denotes orange juice, O denotes Orange, and C denotes coffee. Assume that PO = 10 and Pc = 8. Calculate the equilibrium price and quantity in the Orange juice market. Suppose that a poor harvest season raises the price of oranges to Po = 15 Is it possible to reach a market equilibrium if the price of orange juice PJ remains unchanged? Why? How much quantity of orange juice will finally be exchanged on the market? Find the market price necessary to restore equilibrium. Deduce the equilibrium quantity of orange juice. Draw a graph to illustrate your answers. Q2 Suppose the price elasticity of demand for the market of mobile phones is 0.90. If all mobile-phone companies simultaneously increased their prices, will total revenue in the industry increase or decrease? If a single mobile-phone…Consider the coffee market and the sugar market. Suppose that these two goods are complements. For each of these two goods, the demand curve is decreasing, while the gold curve is increasing. If the demand for coffee increases, then the equilibrium market price for sugar : a)decreased. (b) remains unchanged. (c) increases (d) There is not enough information to conclude.
- 1. Assume you spend your entire income on two goods X & Y with prices given as PX & PY, respectively. Prices and income (I) are exogenous and positive. Given that U = X2 + Y2 , derive the Marshallian demand function for good Y and evaluate the type of good. 2. Assume you spend your entire income on two goods X & Y with prices given as PX & PY, respectively. Prices and income (I) are exogenous and positive. Given that U= X2Y2 , derive the Hicksian demand function for good Y.3. Suppose that initially PX = 2, PY = 8, I = 96 and the Marshallian demand function for good Y is given by Y∗ = (0.5I/ PY)+(0.5PX/PY)− 0.5. Calculate the own price & income elasticities of demand for good Y. Interpret your computed values and say something about the type of good.4. Suppose the economy has 100 units each of goods X and Y and the utility functions of the (only) 2 individuals are: UA (XA,YA) = X0.25Y0.75, UB (XB,YB) = X0.75Y 0.25Show that pareto-improvement is possible if,…Consider a two-city (A and B) regional economy where each city operates on the negatively sloped portion of its utility curve. In the initial equilibrium, the two cities are identical. Then air pollution (lead emissions) in city B decreases the brain power and productivity of workers in the city by 20 percent. Illustrate the effects of lead emissions on the regional equilibrium, indicating the direction of changes in city size (the number of workers) and regional utility.Below is an edgeworth box of two individuals, Ross and Rosa, in the consumption of two goods, X and Y 1. Consider allocations b-f (meaning points a, b, and f). Which allocations(s)A. are better for Ross than “a” (ignoring Rosa)?B. are better for Rosa than “a” (ignoring Ross)?C. are worse for both Ross and Rosa than “a”?D. are better for both Ross and Rosa than “a”?E. are Pareto superior to “a”?2. Suppose that the initial allocation is point a between Ross and Rosa.A. Discuss how Ross’s condition be made better off without harming Rosa(i.e., Rosa maintains her level of utility).B. Illustrate this in a separate diagram and label point/s as necessary (also,if other point/s will have to be made or incorporated).3. Consider once again that the initial allocation is point a. A. Discuss (very briefly) how point d is reached as a Pareto efficientallocation between Ross and Rosa.B. illustrate this condition in a separate diagram.4. Consider points b, c, d, and e. Now plot the utility…