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Unformatted text preview: Optimal allocations of factors K and L between two producers, Producer X & Producer Y To combine these efficiencies into our Production Economy we use the following general strategy: [1] Take the quantities of aggregate factor endowments K and L as exogenously given. [2] Solve the production side for Pareto Optimal factor allocations, and hence the corresponding output levels X and Y on the PPF (production possibility frontier). This ensures the production efficiency in the economy. [3] Using the output levels of X and Y produced, we then solve the exchange economy to generate Pareto Optimal goods allocations, and hence the corresponding utility possibility frontier (UPF). This ensures the consumption (or exchange) efficiency in the economy. [4] We then impose additional conditions so that the production allocations are compatible with the exchange allocations. This will ensure the overall efficiency in the economy. Okay. 180 Now, analytically, we can describe the Pareto Optimal Production economy using 9 equations outlining the Pareto Optimal conditions of the economy as follows: Given aggregate factor endowments, K and L, we want to find... allocations (XA, XB, YA, YB) of goods allocations (KX, KY, LX, LY) of factors which satisfy the following conditions. KX + KY = K LX + LY = L MRTSX = MRTSY (= MRTS) (1) (2) (3) These first three equations (1), (2), and (3) make up the production side efficiencies. This gives us our PPF. XA + XB = X YA + YB = Y MRSA = MRSB (= MRS) (4) (5) (6) These three equations (4), (5), and (6) make up the consumption side efficiencies. This gives us our UPF. And, of course we need the production functions... X = f(KX, LX) Y = g(KY, LY) (7) (8) As well, we need the mysterious 9th equation that ensures the Overall Efficiency Requirement... MRS = MRT (9) While the consumption side uses MRS and the production side uses MRTS to determine efficient allocations, we cannot equate these measures to ensure overall efficiency. This stems from the fact that we cannot compare the two different object categories, namely MRS which is measured in term...
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This note was uploaded on 05/25/2010 for the course ECON 301 taught by Professor Sning during the Spring '10 term at University of Warsaw.

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