In an exchange economy, there are two people, A and B, and two goods, x and y. The utility functions of A and B are given by u;=xy; for i=A, B. Person A starts with 72.000 units of x and zero units of y. Person B starts with zero units of x and 8.000 units of y. If the price of good y is 1, what is the competitive equilibrium of good x?

Assume that there is two-person two-commodity pure exchange economy. A's utility function is u^ (x,x) = x + ln x2 and his endowment is w4 = (1,4). B's utility function is u²(x,x) = x + 2 In x2 and his endowment is w = (3,2). (a) Determine and draw the set of Pareto efficient allocations in an Edgeworth box for this economy (b) The price p₂ is normalized to 1; for simplicity we write p, as just p. Calculate the Walras equilibrium pricep and Walras allocation [(4,2), (2)]. Check that the Walras allocation is Pareto efficient graphically and algebraically.

χν 2yD/xD for David and MRSS xy 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 MRS M = 2yM/XM for Mohammed, MRSxy Ys/xs 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…

D7) In a two good two consumer economy, utility functions are U1(x1,x2) =x1(x2)2 and U2(x1,x2) = (x1)2 x2 The endowments of the consumers are e1 =(10,0) and e2=(0,20). Find the allocation of goods in Walrasian equilibrium.