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Question 3 Consider a standard production economy (J,J, (u', when, (hea, (s" )(neaxa) where at least one of the agents has strictly monotone preferences. Recall that an allocation is a pair (x, y) = (x',....x, y' , ...,y'je(R!)' x (RL)I such that y' E Y' for each j, and ), x = ), wi + ); y'; and that allocation (x, y) is Pareto efficient if there does not exist another allocation (x, y) such that u' (x ) > ul(x' ) for all consumers, with strict inequality for some. A profile of production plans y = (y', ..., y') is feasible if y' E Y for each j; a feasible profile of production plans is technically efficient if there does not exist an alternative feasible plan y such that , y' > >; y'. Also, given a profile y of production plans, a profile x = (x',..., x') of consumption bundles is feasible if E x' = [: wi + ), y'. Finally, feasible profile x is allocatingely efficient, given y, if there does not exist an alternative profile & that is also feasible given y and such that u' ($ ) > ul (x' ) for all consumers, with strict inequality for some. Given these definitions: 1. Argue that if (x, y) is Pareto efficient, then profile y is technically efficient (since one agent has strictly monotone preferences). 2. Argue that if (x, y) is Pareto efficient, then profile x is feasible and allocationefficient given y. 3. In what follows you will argue that, even together, technical and allocation efficiency don't suffice to guarantee Pareto efficiency. Suppose that there are two commodities, two individuals and one firm. Both individuals have smooth utility functions, while the technology of the firm is Y = ((y1, yz) ER, x R_ ly,