General Equilibrium

Question 1

Equilibrium condition

Answer 1

Demand=supply

Question 2

Rearrange to find sum of net demand to =0

I.e amount supplied by one person= amount demanded by the other

Question 3

Define net demand functions

Question 4

Sum net demand functions to get aggregate net demand functions for each good.

Answer 4

Aggregate net demand (Z) should = 0

Question 5

So now we have 3 key points equivalent to one another.

Why do this?

Answer 5

Shows an equilibrium exists.

Question 6

We can skip this, how?

Answer 6

Prove in a single market through Walras’ Law

Question 7

Walras’ law

Answer 7

If prices are non-zero,

Question 8

So we only need one equation. How do we find 2 prices with one equation.

Answer 8

Find relative prices. Multiply both prices by 1/p₂

Question 9

When will a equilbrium set of prices exist?

Answer 9

As long as net demand is continuous.

I.e as long as a change in price causes a small change in QD, (not a big jump) , we can find an equilibrium set of prices.

Question 10

What assumption does this existence of equilibrium also depend on?

Answer 10

Many consumers and each small relative to size of market.

So as long as aggregate net demand is continuous and this assumption holds… there will be an equilibrium set of prices.

Question 11

Numerical steps