182 the production side of the model first we solve

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Unformatted text preview: cs courses except for the following difference...previously, you were asked to accept the PPF as exogenously given while here, the PPF is analytically derived from the solution of the Pareto Optimal allocation problem. We have reached the point 183 now where we do not need to take this result (the PPF) as a primitive or primal concept but can use the basic concept of Pareto Optimality and derive the PPF as a consequence. Pretty cool, huh? Now that we have the production side of the economy all solved and summarized in the PPF, we can proceed to solve the remaining four equations to get the consumption efficiency and overall efficiency. XA + XB = X YA + YB = Y MRSA = MRSB MRS = MRT (= MRS) (4) (5) (6) (9) Solving these we find all possible Pareto optimal allocations (XA, XB, YA, YB) of goods. That is, we solve the pure exchange economy for every point on the PPF while making sure that the overall efficiency condition is also satisfied: [1] We move along the PPF to maintain the production efficiency. [2] For each point on the PPF, we can solve the pure exchange economy to obtain consumption efficiency at that point. Since the output levels X and Y vary as we move along the PPF, the dimensions of the Edgeworth box will vary accordingly. Each point on the PPF has a different Edgeworth box having different dimensions. Of course, each associated pure exchange solution provides a contract curve of Pareto Optimal allocations of goods (and the corresponding UPF). [3] To ensure the overall efficiency condition, we need to find a point on the contract curve at which the common MRS (slope of the indifference curves) is equal to the slope of the PPF (MRT). 184 Y MRT MRT PPF X {Common slope of ICs} = {Slope of the production possibility frontier (PPF)} MRS = MRT [4] Each point of the PPF produces an individual utility possibility frontier (UPF) since the Pareto Optimal solutions of the pure exchange economy (contract curve) can be converted to utility levels. Since there are infinitely many points on the PPF, there will be infinitely many corresponding UPFs. UB Gran...
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