General Equilibrium Conditions In The Classical Model

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Intermediate Macro Economics (W3213)
Prof Xavier Sala-i-Martin
Chapter 6
6.1 General Equilibrium
General Equilibrium Conditions in the Classical Model
We have seen THREE markets so far: Cookies (Goods), Bonds and Money.
We will assume that the prices of our model (namely, the real interest rate and the price level) adjust to clear the three markets: real market, bond market and money market.
Equilibrium in each market would mean:
(a) Yst (r,...) = Ydt (r,...) [Goods Market clearing condition]
(b) Bt=0 [Bond Market clearing Condition]
(c) Mst=Mdt=PL(R,Y,ψ) [Money Market Clearing Condition]
Recall from Microeconomic Theory that the price of artichokes moves to clear the artichoke market. The price of bananas moves to clear the banana market. Following this reasoning, how can we think of TWO PRICES (r and P) clearing THREE MARKETS simultaneously? (In mathematical terms, there are THREE EQUATIONS and TWO UNKNOWNS. So it appears that we cannot solve this system. This seems to be a big problem. Luckily, Leon Walras developed a theorem that will help us in this regard.
6.2 Walras’s Law
If IBC of a family holds,

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