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Fisher Equation: An Important Economic Relation

April 13, 2012 | Comments: 0 | Views: 172

P*G=M*V is a relation explaining the quantitative theory of money. P stands for the price levels in the economy; V stands for velocity of money in the economy; M is the supply of money and G is the GDP of the economy. Now the relation was given by economist Fisher specifying the relationship between the various variables as explained above. (^ stands for change in quantity in the article.)

It was Milton Friedman who recognized the true appreciation of the above equation. As supply of money increases the price levels increases keeping the other variables constant. And when the supply of the money decreases in the economy the general price levels decreases in the economy keeping other two variables constant. This mathematical relationship gave rise to the monetary policies as practiced by the central banks to control inflation so if there is high inflation in the economy simply decrease the money supply by increasing the interest rates. By increasing the interest rates there is less lending of money in the economy and more investing thereby less money in the economy. Thus increased interest rates decrease the supply of money and bring the inflation or the high price levels back to normal levels as indicated by the fisher relation.

Also there might be the case when there is very low activity in the economy and govt. wants to restore the investors' confidence by supplying more money M in the economy which would lead the central banks to decrease the interest rates and thus give more lending for investments. This according to fisher relation finally increases the price levels to high levels in the long run. Thereby increasing the inflation again but govt. wants to make sure that the inflation level does not reach abnormally high levels and it is at mediocre level only. If inflation reaches very high levels than there could be again an action plan by central bank to increase the interest rates and bring down the inflation to normal level and govt. again must make sure that the inflation does not reaches an abnormally low levels. If inflation reaches high levels than there could be worry among the consumers and the corporations about such high price levels and if inflation reaches very low levels than suppliers and corporates could be affected and there would be decrease in profitable opportunities and thereby bringing down the economy growth rate. Hence a proper balance of inflation by govt. through regulating the interest rates happens periodically by the central banks.

This regulation of interest rates for maintaining the inflation and growth in the economy is the monetary policy. Unlike the fiscal policy monetary policy does not affect the GDP in the long-term but certainly has effect on the price levels in the economy. Sometimes it might happen that few goods have large supply of money that results in inflation and sometimes large amount of goods have little supply of money that results in deflation. Both deflation and inflation are not good for the economy and thus a proper balance between the GDP growth and supply of money needs be there so that no mismatch occurs and proper amount of goods have a proper amount of money. P*^G=V*^M implies that if there is change in the GDP in the short run then it requires extra money created by an amount ^M to avoid the mismatch mentioned above. Thus the extra goods produced in the economy have an extra supply of money.

^P*G=V*^M is another variation of the equation which implies that if GDP does not increase or remains constant then with the ^M increase in the supply of money the price levels increase by ^P which can result in inflation if GDP does not grow by ^G to compensate for the extra supply of money in the economy. If we combine the equations and assuming that velocity of money to remain constant in the economy then it results in the relation P*^G+^P*G =V*^M, so if money supply changes by ^M,then part of the supply is offset by growth in the economy ^G and part by the ^P the change in price levels. So overall the inflation created is too low when compared to inflation created when the ^G is low or fairly constant.

The equation P*^G+^P*G =V*^M has an analogy the stock markets so when there is no great change in GDP in the short run and large amount of money goes in the stock market so that change in ^M is large and ^G is low, from the equation the ^P also increases. These ^P the price levels of the stocks reaches abnormal highs. In short run the market cannot realize such a big change in GDP but it takes large amount of time to cause this large change in GDP so in short time it is not possible to realize such large change in GDP. Investors anticipating such large change in GDP in a short duration of time invest too much there by increasing the ^M in the short run which causes the price levels to change appreciably. This was clear in the dot-com bubble when the IT companies were growing companies new on the horizon, investors anticipated large change in GDP caused by the growth of these companies in a short time but that did not materialized in the short-term which resulted in a sort of bubble which finally busted and the irrational exuberance of the investors ended. Here also there was a mismatch between the GDP growth and money supply that created this sort of bubble and because this mismatch was a result of irrational reasons no one checked it or care about it.

In equation P*^G+^P*G =V*^M if there is constant money supply then ^M=0 this implies that P*^G+^P*G=0 which implies P*^G=-^P*G. If a GDP increase by ^G then price levels ^P goes down this means that now goods are selling at lower prices. This would ultimately affect the profits of the corporates and this demands ^M be raised or money supply by the govt. to restore the goods and services to their earlier values and not thus affect the investments and profits in the economy.

Another variation of the equation could be P*^G+^P*G =V*^M + ^V*M specifies that change in GDP and price levels together influences the money supply and velocity of money in the economy. Therefore the variations in GDP or variations in prices in the economy leads the policy be adopted by the central banks to keep up growth and inflation in the economy. If there is no change in money supply that is ^M=0 then above equation becomes P*^G+^P*G= M*^V, so a change in V depends on the growth in the economy or the general price levels change or both. Everything goes fast paced and money in form of credit cards, debit cards, cash and other forms increases in a rapid way between customers and sellers.

Lowering of credit terms in the recent depression of 2008 called the real estate bubble was the major contributor of financial disaster. There was an increase of credit to borrowers to buy houses and they were on easy terms. Borrowers with bad history and poor credit records were given loans. The interest rates charged were also not too high so there was an increase in supply of money in the US economy which increases ^M. So ^M is the increase in the loan money in the hands of the customers due to real estate euphoria which was prevailing in US prior to 2007. Also there were Mortgage backed securities which repackaged loans to investors by giving them interest on loans. Hence indirectly there was more encouragement to the banks to grant loans to the borrowers since they laid off the liabilities in the form of loans to the mortgage-backed securities investors. There was rapid financing and refinancing of loans by the borrowers seeing that once they finance loans to buy home they can resell the houses at higher prices and can refinance the loans by giving back the earlier loan thereby in between making some money for themselves. This resulted in an increase of the credit money in the economy by ^V. Also the US economy was not growing that much prior to the depression so a bubble in real estate prices was unreasonable. Hence we assume that ^G is small compared to other increases as mentioned before. The equation P*^G+^P*G =^M*V+M*^V implies ^P=(V*^M + ^V*M- P*^G)/G which implies if ^M and ^V are large as explained before and ^G is small then overall ^P is very high hence there was a bubble in the economy. However if there was the case that GDP of US was growing very rapidly than the effect of change in money supply and velocity of money could have been off-set to some extent and the real estate prices would had been much more realistic. But that was not the case and real estate prices grew out of nowhere and their very high prices were irrational and unrealistic without any sound economical basis. Hence the bubble resulted which spread to the entire globe and brought about one of the worst recessions since the 1929 great depression. The 2008 depression led to crash of major investment banks, loss of jobs, loss of wealth, loss of global economy. The crisis engulfed the entire world and its implications can still be felt today.

P*G=M*V also holds in explaining exchange rates variations with respect to each other. Consider a country X increase its money supply M than from fisher relation the prices will move up thereby a person can buy the same goods at higher price than it was possible earlier. Another country Y has the same money supply maintained by the govt. so that the same goods are selling at the same price as earlier. Now because goods have become more expensive in country X the purchasing power of the currency of X has decreased compared to other country Y purchasing for the same goods. Hence there is decline in the value of the currency of X as compared to Y and thus the exchange rate moves in favor of country Y. If a country decreases its interest rates then it affects the exchange rates and thus value of currencies. If there is a decrease in interest rates than currency loses value but when there is an increase in interest rates the currency gains more value.

P*G=M*V is a wonderful equation which van explain many economic phenomenon happening in our world today. It's the equation which has many economic applications with sound reasoning explaining various economic processes. Like the Einstein's equation of E=m*c*c the importance of the fisher equation has the same if not greater importance in economics.

Very much interested in writing about the topics on finance and science. There is large variety of topics that should be addressed and write about. Have a flair for writing and have written articles on science and finance.

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