## 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