Modern central banks nevertheless don’t fix the money stock and then sitting by passively watching the business cycle. Therefore the derivation of the aggregate curve in the section above is a little distant from modern macro-economies. Once we identify that modern central banks play an active role in managing the macro-economy, the examination of aggregate demand is somewhat different. Modern central banks pay plenty of attention to the inflation rate. When the inflation rate increases the central bank tends to enhance the real interest rate to try to reduce aggregate demand and cool off inflation.
Stanford economist John Taylor at present on leave at the Treasury Department as Undersecretary for International Affairs has a simple model of how central banks act called as the Taylor rule. As-per to the Taylor rule the central bank has a target value π for the inflation rate and an estimate r* of what the normal real interest rate must be. If inflation is elevated than its target value the central bank raises the real interest rate above r* when inflation is lower than its target value, the central bank lesser the interest rate below r* according to a rule:
r = r* + Φ' x (π - π') Where the parameter Φ' determines how forcefully the central bank reacts to inflation.
We acquire the Taylor rule the model of how the central bank acts as well as substitute its expression for the determinants of the real interest rate into the IS-curve equation:
This equation is too multifaceted to work with so once more it is useful to simplify. Define Y0 to be the level of real GDP while the real interest rate is at its long-run normal value r*:
And describe a new parameter Φ’, the Greek letter ‘phi’ with one apostrophe affixed to it to be:
Then we are able to write our combination of the Taylor rule and the IS curve in the simple looking form:
Which is called as the monetary policy reaction function and which is shown in Figure.
This financial policy reaction function looks akin to the aggregate demand curve of the previous section. When prices raise in this case, when inflation is elevated than the central bank want it to be real GDP declines. There are but differences. The aggregate demand curve of the preceding section was a relationship between the price level and real GDP. This financial policy reaction function is a relationship between the inflation rate and real GDP. The aggregate demand curve implicated that the Federal Reserve sat like a potted plant while the business cycle proceeded. The financial policy reaction function assumes that the Federal Reserve is engaged in the economy, trying to handle it to keep inflation close to the inflation target. Last, the financial policy reaction function is a good model of how central banks actually behave.
The Monetary Policy Reaction Function:
Legend: The proceedings of an inflation-fighting central bank lead to the same kind of downward-sloping relationship between prices as well as output as in the previous section. However in this case it is a higher inflation rate, not a higher price stage that associated with lower real GDP.
Once more nevertheless this monetary policy reaction function offers a glimpse into how over time adjustments in prices as well as wages might carry the economy from the sticky-price equilibrium in which there is unemployment and a gap between GDP and potential output back to the flexible-price equilibrium in which real GDP is equal to potential output. If real GDP is fewer than potential output inflation might fall over time and the central bank reducing interest rates in response to low inflation would carry the economy down and to the right along the financial policy reaction function, rising real GDP. If real GDP is greater than possible output inflation might rise over time as well as the central bank raising interest rates in response to high inflation would carry the economy up as well as to the left along the aggregate demand curve reducing real GDP.
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