Lecture11

# Lecture11 - ECON 301 LECTURE #11 PARETO OPTIMAL THEORY...

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1 ECON 301 – LECTURE #11 PARETO OPTIMAL THEORY PRODUCTION ECONOMY Now let’s extend our Pareto Optimal concept to a production economy… Two Goods Good X Good Y Two Factors Capital (K) Labour (L) Two Consumers Consumer A Consumer B We need to consider both the exchange efficiencies and the production efficiencies in this framework. EXCHANGE EFFICIENCY PRODUCTION EFFICIENCY Given exogenously fixed quantities of Given exogenously fixed quantities aggregate goods endowments X and Y, of aggregate factor endowments K the pure exchange economy provides and L, the production side will Pareto Optimal allocations of goods X provide Pareto Optimal allocations between consumers A and B. 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. Now, analytically, we can describe the Pareto Optimal Production economy using 9 equations outlining the Pareto Optimal conditions of the economy as follows:

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Given aggregate factor endowments, K and L, we want to find… allocations (X A , X B , Y A , Y B ) of goods allocations (K X , K Y , L X , L Y ) of factors which satisfy the following conditions. K X + K Y = K (1) L X + L Y = L (2) MRTS X = MRTS Y (= MRTS) (3) These first three equations (1), (2), and (3) make up the production side efficiencies. This gives us our PPF. X A + X B = X (4) Y A + Y B = Y (5) MRS A = MRS B (= MRS) (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 (K X , L X ) (7) Y = g (K Y , L Y ) (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 terms of goods and MRTS which is measured in terms of factors. Instead we must equate MRS = MRT which are both measured in terms of goods. So let’s investigate the logic behind the overall efficiency requirement that MRS =
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## This note was uploaded on 03/28/2010 for the course ECON 301 taught by Professor Coreyvandewaal during the Winter '09 term at Waterloo.

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Lecture11 - ECON 301 LECTURE #11 PARETO OPTIMAL THEORY...

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