"The Fed should simply increase the money supply at the same rate that the full employment economy grows, and the government should desist from any stabilizing urges." What school of thought would make this suggestion, and how do economists of that school justify that prescription?

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The school of thought that would make this suggestion is known as the "Monetarist" school of economics. Monetarists believe that the most important role of the Federal Reserve (the Fed) is to control the money supply in order to stabilize the economy. They argue that the central bank should increase the money supply at a consistent and predictable rate that matches the rate of economic growth in order to achieve long-term stability and prevent inflation.

Monetarists justify this prescription using the Quantity Theory of Money, which states that the price level in an economy is directly proportional to the amount of money in circulation. According to this theory, if the money supply grows at the same rate as the full employment economy, the price level remains stable.

Monetarists also argue that stable and predictable monetary policy can encourage investment and long-term planning by individuals and businesses. They believe that by controlling inflation, the central bank can provide a stable environment for economic growth without the need for discretionary government intervention or "stabilizing urges."

In summary, the monetarist school of thought suggests that the Fed should increase the money supply at the same rate as the full employment economy to achieve long-term stability and prevent inflation. They use the Quantity Theory of Money and argue that stable monetary policy can promote economic growth without the need for government intervention.