(7 marks) Assuming that velocity and output were fixed, the basic Quantity Theory implies inflation equals the growth rate of the money supply, r(t) = %dM(t). a) (1 mark) Derive this relationship from the equation of exchange. b) (2 marks) Under the basic Quantity Theory, what is the functional relationship between the rate of return on money and the growth rate of the money supply? If the rate of growth of the money supply is -12%, what is the rate or return on money? (in your answer write %d12(t) as %d0(t)) During the Great Depression, the price level at end of 1929 is P(1929) = 1, and the value of money increases by 50% over the two years from the end of 1929 to end of 1931. c) (3 marks) What is the implied price level at the end of 1931? What is the average inflation rate from the end of 1929 to 1931? What is the average rate or return on money from the end of 1929 to 1931? In reality rates neither output nor velocity were constant. From the end of 1930 to the end of 1931, output falls by 17%, velocity falls by 12% and the price level fell 10%. (Hint: use equation of exchange) d) (1 mark) What is the implied growth rate of the money supply in 1931