Suppose the economy is characterized by the following equations.IS curve: r = 20.20 - 0.002YLM curve: M/P = Y - 250(r + ?e)SRAS curve: Y = + 100(P - Pe)The nominal money supply is M = 19,800, expected inflation is ?e = 0.20, and full-employment output is 
= 10,000.(a)If the economy begins in general equilibrium, what are the equilibrium values of the price level, output, and the real interest rate?(b)If the expected price level is the price level you found in part (a), what happens to the price level, output, and the real interest rate in the short run if there's an unanticipated decrease in the nominal money supply to 14,737.5? {Hint: guess some price levels
that differ from the one you found in part (a) by increments of 0.25.}(c)If the expected price level is the price level you found in part (a), what happens to the price level, output, and the real interest rate in the short run if there's an unanticipated increase in the nominal money supply to 24,937.5?
What will be an ideal response?
| (a) | From the IS curve with Y = 10,000: |
Combining the IS curve with the LM curve gives the AD curve, with values for output set at full-employment output (Y = 10,000), and with the price level equal to the expected price level:
M/P = Y - 250(r + ?e)
19,800/P = 10,000 - 250(0.2 + 0.2) = 9900, so P = 2.
| (b) | Now P may differ from Pe in the short run, so things are a bit more complicated. Combining the |
AD: M/P = Y - 250(r + ?e)
= Y - 250[(20.20 - 0.002Y) + 0.2]
= 1.5Y - 5100.
SRAS: Y = 10,000 + 100(P - 2)
Plug SRAS into AD to get:
M/P = 1.5Y - 5100
= 1.5[10,000 + 100(P - 2)] - 5100
= 9600 + 150P
This is a quadratic equation in P for a given M, as you can see by multiplying through by P and rearranging:
150P2 + 9600P - M = 0
Note that in part (a), with M = 19,800, the solution to the equation is P = 2.
With M = 14,737.5, we need to solve the equation 150P2 + 9600P - 14,737.5 = 0. You can use the quadratic formula, or guess the solution by checking increments of P of .25, to find P = 1.5. Output is Y = 10,000 + 100(P - 2) = 9950. The real interest rate is r = 20.20 - 0.002Y = 0.30.
| (c) | With M = 24,937.5, we need to solve the equation 150P2 + 9600P - 24,937.5 = 0, which has the |
The real interest rate is r = 20.20 - 0.002Y = 0.10.
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