1) Income velocity V is the number of times per year an average dollar in the money supply changes hands in transactions involving final goods and services. It is equal to: V = PY/M Multiplying both sides of this equation by money M yields the quantity equation: MV = PY a) Using the following data for 2008 to calculate income velocity. Real GDP = Y = $11,671 billion The GDP deflator = P = 1.225 M =$7,671.6 billion b) Multiply this value of I by the value for M in 2008 and verify that MV = PY. c) Recall from class that the percentage change in the product of two variables is approximately equal to the sum of the percentage change in each of the variables. Appling this approximation to both sides of the previous equation yields: % Change in M + % Change in V= % Change in P + % Change in Y To confirm this approximation, consider the data in the following table. (1) (2) (3) (4) (5) (6) (7) (8) (9) % % Period M Change V Change P Change Y Change in M in V in F in 1 100 2.0 1.0 200 2 104 2.02 1.03 204 Calculate the percentage changes in each of the variables in the above table. Now, substitute the percentages into the above equation (% Change in M + % Change in V = % Change in P + % Change in 1) and verify that the percentage change version of the quantity equation is accurate. d) Starting again at Period 1, calculate I for Period 2 in the table below. Compute the percentage changes. Substitute the percentages into the equation (% Change in M + % Change in V=% Change in P + % Change in 1) and once again verify that the percentage change version is a reliable approximation. (1) (2) (3) (4) (5) (6) (7) (8) (9) % % % % Period M Change A Change P Change Y Change in M in V in F in Y 100 2.0 1.0 200 2 108 1.06 1942) The simple quantity theory of money assumes that velocity is relatively constant and that real GDP increases at its long-run rate of growth Over the past few decades, the long-run growth rate of real GDP has been about 3 percent per year. This 3 percent figure is the result of changes in population, resources, and technology, which are all typically viewed as exogenous. a) Substitution these values into the percentage change version of the quantity equation yields % Change in M + = % Change in P + Or, upon rearranging, % Change in P = % Change in M - This equation indicates that, according to the quantity theory, the rate of inflation will be equal to the growth rate of the money supply minus the long-run rate of growth of output. b) Given the assumptions in Part a concerning velocity and real GDP growth, complete Columns 4, 5, 8 and 9 in the table below for four periods. (1) (2) (3) (4) (5) (6) (7) (8) (9) % a Period M Change V Change P Change Y Change in M in V in P in Y 1 100 2.0 1.0 200 3 0 3 2 103 2.0 206 3 97.85 4 101.76 c) Use the data in Column 2 of the above table to complete Column 3. Now, use the above equation to complete Column 7. Finally, use your approximations of the percentage changes in P in Column 7 to estimate the price levels in Column 6. d) Using the exact quantity equation MV = PY and the levels of M, V, and Y in Columns 2, 4, and 8, calculate the exact price level in each period and compare these answers with your estimates in Column 6. Note how the percentage change version of the quantity equation is a good approximation of the percentage changes in the above table
