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Unformatted text preview: Disclaimer: These notes were prepared based on lectures of Prof Sala-i-Martin’s 2008 Fall Course of Intermediate Macro-W3213. Contents of these notes might not match completely with the current teachings in class. An updated version would be available later in the semester. 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) Y s t (r,...) = Y d t (r,...) [Goods Market clearing condition] (b) B t =0 [Bond Market clearing Condition] (c) M s t =M d t =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, ? + 1 ¡ + ¢ 1 + ?£ = ? 1 + ? 1 + ¢ 1 6. 1 Where the LHS gives the total resources available and RHS gives the total uses of the resources. M is the money available at the beginning of the year (Money Supply) and M 1 is the money we want to have at the end of the year (money demand). Imagine that markets cleared last year (so B =0). Walras’ Law says that in general assume the budget constrained is satisfied, then if n-1 markets clear the n th market should also clear. Here we are dealing with 3 markets: goods market, money market and bonds market. That is, if TWO of the markets clear, then the other market clears also! Thus we can study the behavior of TWO markets and make sure that they clear, and we know that the other market will clear also. Walras’ Law implies, if the goods market and the money market clear, then the bonds market should necessarily clear. If Y d =Y s AND M 0= M 1 , THEN B 1 =0 . We choose REAL (Goods) and MONEY markets and do not explicitly consider the bonds market because we know that it the goods and money market are in equilibrium then the bonds market will be in equilibrium from Walsras’ law. Now we analyze how they work....
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This note was uploaded on 11/10/2011 for the course ECON 3100 taught by Professor Sala-i-martin during the Spring '11 term at Columbia.
- Spring '11