6. 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 MRSxy = 2yM/XM for Mohammed, MRSy = 2yp/XD for David and MRS.y = 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. (4 marks) 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 substitution of labour for capital is 2. Is the current production of the two firms efficient? If not, describe an exchange of inputs that would improve efficiency. Can these production levels of the two firms be observed in a perfectly competitive equilibrium of a production and exchange economy? Explain. (4 marks)