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Consider an economy in which the long-run price level and inflation rate are determined according to the quantity theory of money.

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HA 6 is the question please check the problem, 

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Consider an economy in which the long-run price level and inflation rate are determined according to the quantity theory of money. Assume that the velocity of money V is constant, the supply of money Mt is controlled by the central bank, and long-run output Yt is exogenously driven by technological progress.

  1.        Thanks to technological progress, output doubles in this economy relative to previous year. Yet the central bank only increases the money supply by 40%. What will happen to the price level, that is, by how much will it change? What should the central bank have done in order to keep the price level unchanged relative to previous year? 
  2. Now assume that the rate of economic growth in this economy is equal to 2% per year. What is the rate of inflation if the central bank increases money supply at a rate of 3% per year? What should the central bank do in order to maintain inflation at 2% per year? 
  3. Suppose that the central bank is expanding money supply at a rate of 3% per year. Under this policy, the observed rate of inflation in the economy is also equal to 3% per year. What does this imply about the rate of economic growth? 

Problem 2. Consider an economy in which the consumer price index was equal to 121 for the year 2012 and 110 for the year 2011, with 2010 taken as benchmark (CPI = 100). 

  1. Calculate the rate of inflation for the years 2011 and 2012. 
  2. Assume that the rate of inflation is constant at the rate found in part 1 (yes, it should be the same for both years). Assume, in addition, that the growth rate of real GDP is 3% per year, and money velocity is constant. According to the quantity theory, what is the growth rate of money supply in this economy? 
  3. The central bank is unhappy about high inflation in the economy and wants it to be at 5% (yes, your answer to part 1 should be greater than 5%). What should the new growth rate of money supply be to keep inflation at that desired level?