wo individuals, Fred and Helen, are in an economy with no production, and each have the utility function U = 10XY. Prices of both X and Y are set at $1. Initial endowments for Fred are 10 units of X and 6 units of Y. Helen has 8 units of X and 12 units of Y. Find the general equilibrium prices and allocation, then show that the G.E. allocation is Pareto efficient.

a) Consider an economy with 3 agents, Mohammed (M), David (D) and Susan (S). There are two goods available, good x, and good y. The marginal rates of substitution (where good x is on the horizontal axis and good y is on the vertical axis) are given by for Mohammed,  for David and  for  Mohammed and David are both consuming twice as much of the good x than good y, while Susan is consuming equal amounts of x and y. What are the conditions for Pareto efficiency in an exchange economy? Are these consumption levels economically efficient?  Can these consumption allocations be observed in a perfectly competitive equilibrium in an exchange economy without production? Explain.   b) There are two firms in the economy. Each firm employs positive amounts of capital and labour. The technology satisfies diminishing marginal rate of technical substitution of labour for capital. Currently, A’s marginal rate of technical substitution of labour for capital is 4 while B’s marginal rate of technical…

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Anthony and Brandon have a utility possibility frontier that is given by the following equation: UA + 2U}? = 50. Anthony and Brandon believe that the ideal allocation is given by maximizing an appropriate social welfare function. Anthony thinks that UA = 30 and Ug = 100 is the best distribution of welfare, and presents the maximization solution to a weighted-sum-of-the-utilities social welfare function that confirms this observation. Anthony's social welfare function can be written as a) W = UA + UB b) W = UA + 10UB c) W = 10UA + UB d) W = 2UA + 10UB e) None of the above.

2(a) Suppose x is a Pareto efficient allocation in which each agent holds a positive amount of each good. Also suppose that preferences are convex, continuous and monotonic. Then show that x' is a Walrasian equilibrium for the initial endowments that are redistributed such that w, = x' for i =1,.n.

Consider the pure exchange economy with 2 goods, good 1 and good 2, and two consumers, consumer A and consumer B. Consumer A is initially endowed with 10 units of good 1 and 10 units of good 2. Consumer B is initially endowed with 2 units of good 1 and 2 units of good 2. The consumers have the following utility functions: ua(X1a,X2a)=X1AX2A²; uB(x1B,X2B)=X1B+X2g. Among the prices below, which ones are Walrasian equilibrium prices? O a. p1=3, p2 =2 O b. p1=4, P2 =5 O C. None of the other answers. O d. p1=5, p2 =4 O e. P1=2, p2 =3

4) preferences represented by U, (x11, x21) = x11X21. Agent 2 has preferences represented by utility function U2(x12, xX22) = X12X22. The initial endowments are wi = (1,3) and w2 = (3,1). Show directly that every interior Pareto optimal allocation in this economy is a price equilibrium with transfers by finding the associated prices and transfers. Consider a two agent and two good exchange economy where agent 1 has

Consider a Robinson Crusoe Economy. There are two commodities in the economy: one is labor L and the other is yam y. The producer Crusoe has production technology of y = Lî. The consumer Crusoe's preference is represented by y(1 – L)¿ where L is the supply of labor. The consumer Cruose has all the share of the producer Crusoe's profit. (a) Find efficient allocation (L, y). (b) Define and calculate a competitive equilibrium of the economy. (Normalize the wage to be unity, i.e., w = 1).

The First Theorem of Welfare Economics can be expressed asA) the competitive equilibrium results only when no transactions costs exist.B) the competitive equilibrium does not involve reallocation of endowments.C) any efficient allocations can be achieved by competition.D) the competitive equilibrium is efficient.

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.