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Unformatted text preview: for good X XA + XB = X Market equilibrium for good Y YA + YB = Y (OPTIMAL CONDITIONS) Pareto optimality for both Person A and B MRSA = MRSB Inside the Edgeworth Box XA + XB = X Inside the Edgeworth Box YA + YB = Y We can clearly see that the Walrasian pure exchange solution (competitive equilibrium) does indeed satisfy the optimality condition MRSA = MRSB of the Pareto optimal pure exchange model since at the competitive equilibrium, both of the consumers equate their marginal rates of substitution to the common price ratio 199 MRSA = MRSB = PX PY In other words, the general equilibrium solution provided by solving the Walrasian competitive equilibrium is also an optimal solution (along with many other possible solutions) of the Pareto Optimal pure exchange model. The key link is the common price ratio, PX. PY So I bet you're wondering what the First Fundamental Theorem of Welfare Economics has to say about the Production Economy... For a Production Economy with 2 goods (X,Y) and two factors (K,L) and two consumers (A,B) we have studied both the Walrasian general equilibrium model and the Pareto optimal model. Let's compare the logical structure of the two models side-by-side:
WALRASIAN PRODUCTION MODEL PARETO OPTIMAL PRODUCTION MODEL (EQUILIBRIUM CONDITIONS) Consumer Equilibrium for Person A MRSA = PX PY PXXA + PYYA = MA Consumer Equilibrium for Person B MRSB = PX PY PXXB + PYYB = MB Producer Equilibrium for Producer X MRTSX = r w X = f(KX, LX) Producer Equilibrium for Producer Y MRTSY = r w Y = g(KY, LY) (OPTIMAL CONDITIONS) Pareto optimality for both Person A and B MRSA = MRSB Production efficiency MRTSX = MRTSY X = f(KX, LX) Y = g(KY, LY) 200 Zero Profit Conditions PX = rkX + wlX PY = rkY + wlY Market equilibrium for goods XA + XB = X YA + YB = Y Market equilibrium for factors KX + KY = K LX + LY = L Inside the Edgeworth Box for goods XA + XB = X YA + YB = Y Inside the Edgeworth Box for factors KX + KY = K LX + LY = L Overall efficiency MRS = MRT We can show that the equilibrium conditions o...
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- Spring '10