Econ 337 #4

# Econ 337 #4 - Model 1 Pure Exchange Economy An economy with...

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Model 1: Pure Exchange Economy An economy with 1. 2 people: Adam & Eve 2. 2 commodities: Apples & Fig leaves 3. Fixed supply of commodities An Edgeworth Box depicts the distribution of goods between the two people.

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Apple F i g l e a v e s O A O E
Apple F i g l e a v e s O A O E Pareto efficiency Each of the Pareto efficient points is where an indifference curve of Adam is tangent to an indifference curve of Eve.

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Mathematically speaking: Mathematically, the slopes of Adam’s and Eve’s indifference curves are equal. If Adam’s MRS > Eve’s MRS, what would happen? EX: MRS A =3 and MRS E =2 M R S M R S a f A d a m a f E v e =
Model 2: Production Economy In pure exchange economy, assume supplies of commodities were fixed. Now consider scenario where quantities can change . The production possibilities curve (PPF) shows the maximum quantity of fig leaves that can be produced with any given quantity of apples.

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The marginal rate of transformation (MRT) of apples for figs (MRT af ) shows the rate at which the economy can transform apples to fig leaves. It is the absolute value of the slope of the production possibilities curve. For apple production to be increased, fig leaf production must necessarily fall.
The marginal rate of transformation can be written in terms of marginal costs: M R T M C M C a f a f =

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Efficiency with Variable Production With variable production, efficiency requires: M R T M R S M R S a f a f A d a m a f E v e = = If this were not the case, it is possible to make one person better off with an adjustment production. Example: MRT=2/3 vs. MRS=1/3 Hence, this equality is a necessary condition for Pareto efficiency.
! ! ; . 2 . 1 Eve af Adam af af af f a f a f f a a Eve af f a Adam af MRS MRS MRT MRT MC MC P P MC P MC P MRS P P MRS = = = = = = = = In a competitive market in which producers maximizing profits and consumers maximizing utilities… Everyone in the economy is a price taker.

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S D P Q P* Q* In a competitive market in which producers maximizing profits and consumers maximizing utilities…
First Fundamental Theorem of Welfare Economics

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