Question

a. Define the quantity theory of money and show how it is related to the equation of exchange.

b. Why is the nominal interest rate the opportunity cost of holding money? If the Fed makes the quantity of money grow at the same rate as the growth rate of real GDP and velocity does not change, in the long run what happens to the price level and

the inflation rate?

c. Find latest evidence on countries facing exponential growth of its money supply and inflation rates

Answer 1

a. According to the quantity theory of money, the amount of money in circulation or the money supply is directly proportional to the price level of goods and services in the economy. Now, on the basis of the quantity theory of money, the equation of money exchange M*V(T)=P(T)*T where the M and V(T) represent the overall amount of money in circulation over a certain period of time and the transaction velocity of money respectively. The P(T) and T denote the price level of goods and services related to the overall transactions in the economy within a certain time period and the real value of the overall transactions of goods and services in the economy within that concerned time period. The equation of money exchange can also be rewritten as M*V(T)/T=P(T) implying that the price level of goods and services related to the total number of transactions in the economy in a certain time period mathematical depends on or is a function of M, V(T), and T.  Note that according to the modified or rewritten version exchange equation of money as the money supply increase the M will also increase resulting in proportionate or commensurate increase in P(T) and vise-versa, holding everything else constant considering the exogenous variables in the equation reiterating the relationship between money supply and price level of goods and services in the economy.

b. In a general sense, the opportunity cost of holding money implies the foregone cost/value of holding or saving money or the interest payments which could have been obtained by utilizing it or investment it on any alternative asset to get economic gain/return or profit. Now, the nominal interest rate the cost or the value of money without adjusting for the changes in price level of goods and services. It is mathematically calculated as the summation of the real interest rate and the inflation which denotes the growth in price level of goods and services, which essentially determines the real value of money or currency in the economy. Therefore, nominal interest rate basically represents the periodic value or cost of money which could have been earned or obtained if it had been invested to any alternative asset instead of holding or saving it and hence, it represents the foregone or sacrificed opportunity to earn the real value of money as it is unsued or utilized.

The real GDP can be mamathetically represented as Y/P where Y and P are the nominal GDP and the price level of goods and services in the economy. Now, if Fed increases the money supply at the same rate the growth rate of real GDP, it essentially implies that the growth rate of money is equivalent to the growth rate of the ration between Y and P. Now, based on the quantity theory of money we know that the growth rate of money supply+growth rate of V(T)=growth rate of P(T) or the inflation+growth rate of real GDP or in other words, growth rate of money supply=growth rate of P(T) or inflation+growth rate of real GDP-growth rate of V(T). Hence, if the growth rate of money supply is same as or equivalent to the growth rate of real GDP and the growth rate of V(T) is held constant then note that the inflation or the growth rate of P(T) will also remain constant or eventually unchanged.

c. In recent years, some of countries experiencing disconertingly high and excessive levels of inflation rate and money supply growth includes Venezvuela, Zimbabwe, South Suda, North Korea, Argentina, and so on with inflation rates of approximately 282972%, 176%, 56%, 55%, and 54% respectively, based on the 2019 data.

Reference

https://ceoworld.biz/2019/09/03/countries-with-the-highest-inflation-rates-in-the-world-2019/