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macro economics
MACRO ECONOMICS
Classical Dichotomy The classical dichotomy is rooted in the understanding that in the long run, real output is determined by “real” inputs such as labour, capital, natural resources and TFP, but not money. This means that changes in the money supply determine changes in the price level over time, but not real output. However, it is important to remember that the classical dichotomy applies only in the long run. Almost all economists would agree that money and price can have very important real impacts on the economy in the shorter run.
In macroeconomics, the classical dichotomy refers to an idea attributed to classical and pre-Keynesian economics that real and nominal variables can be analyzed separately. To be precise, an economy exhibits the classical dichotomy if real variables such as output and real interest rates can be completely analyzed without considering what is happening to their nominal counterparts, the money value of output and the interest rate. In particular, this means that real GDP and other real variables can be determined without knowing the level of the nominal money supply or the rate of inflation. An economy exhibits the classical dichotomy if money is neutral, affecting only the price level, not real variables
If an economy exhibits the classical dichotomy, then comparative statics analysis can be performed using a Jacobian matrix in block triangular form. That is, suppose we write

where represents some exogenous shocks (changes in productivity, aggregate demand, money supply, etc., ordered so that all real shocks come first), and represents the change in the endogenous variables (output, employment, prices, etc., again listing real variables first). Then the matrix J can be partitioned into submatrices as follows:

In other words, when the classical dichotomy holds, it is possible to calculate how all the real variables change by inverting the submatrix only, thus excluding all nominal variables like money supply

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