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General equilibrium

Partial eq. - supply and demand. Fixed:

        Prices of other commodities

        Incomes

        Profits

In gen eq, they are endogenous. Fixed:

        Preferences

        Population

        Endowments

        Technology

 

Gen eq compostion

1. individuals (ie 1, 2)

2. commodities (ie 1, 2, x (x1, x2), p= (p1, p2)

3. preferences of individuals

4. endowment ei = (ei1, ei2)

If we give the p every individual computes its demand xi (p)

To aggregate xa (p)=sum of xi (p)

zi (p)=xi (p)-ei

Aggregate excess demand za (p)=sum z1 (p)=xa (p)-ea

budget line at p (goes through e)

If you have flat segments in indifference curves. You get set as an answer

zi (p)={xi}-{ei}

px=pea

pza=0

2

Budget line at p going through e

 

 

 


p*x1< xi(p)

p*ei e

2

 

 


z

 

 


p

0

for every p za (p) is convex set. It is continuos and it has the right behaviour as prices tend to the boundary)

When you have nonconvexities, adding more people will allow us to close the gaps. Then an equilibrium in the average will mean an average - some people on both equilibrium.

Continuity - if individuals have strictly positive endowment of each good. Or it also does not occur when nobody is impoverished (value of endowment is 0). Or any division endowment of group one is always >1 for group 2.

 

Eatwell

Walrasian system

1. utility function

2. endowment

3. technology

unit input of coefficient Aij

Aww=280/400

200w+12I=400w

120w+8I=20I

subsistence economy-only one independent equation

Perron Frobenius theorem on nonnegative square matrixes. Only 1 will have a nonnegative solution

commodities that are used to produce others are basics, other are not. Price of non-basics will not change the profit rate.

Data (neoclassical)

1.      utility function

2.      Endowment

Data classical

1.      structure of production (technique)

If you tax basics it will change the profit rate, if you tax gold, profit remains the same

If you add labour that is not produced, then from Frobenios theorem you get an inverse relationship between wages and profit

(1+r) (a11+a21p2)+al1w=1

(1+r) (a21+a22p2)+al2w=p2

3rd frobenious - if any of the coefficients rise then the rate of profit falls

Growth

1. Capital accumulation

2. technological progress

 

1. y=f (k, l) constant return

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