# ps9ans - Economics 202 Principles of Macroeconomics Name...

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Economics 202 Name: _______________ Principles of Macroeconomics Professor Melick Problem Set #9 Due Wednesday April 23, 2008 1. Numerical Problem #2 from Abel and Bernanke Chapter 11, found on pages 432-433. ( ) ( ) 130 0.5 500 100 500 130 0.5 0.5 500 100 500 0.5 230 1000 0.5 0.5 1000 0.5 1000 d d d S Y C G Y Y T r G I r Y Y T r G r IS Y r G T M Y r P M LM Y r P = - - = - + - - - = = - - - + + - = - = - + - = - = + Use IS to replace r in the LM to get the AD curve. ( ) P M T G Y P M Y T G Y P M r Y + - + = + - - + = + = 5 . 0 230 5 . 0 5 . 0 230 5 . 0 1000 5 . 0 Use the fact that in equilibrium 500 = = Y Y to solve for the endogenous variables. ( ) ( ) 85 03 . 0 500 100 500 100 315 03 . 0 500 100 500 5 . 0 130 500 5 . 0 130 03 . 0 1000 30 1000 500 5 . 0 6 1320 1000 5 . 0 6 220 1320 1320 280 500 1320 100 5 . 0 100 230 500 5 . 0 230 = - = - = = - - + = - - + = = = - = - = = = + = + - + = + - + = r I r T Y C r r r Y P M P P P P M T G Y d d for part c) we must modify the IS curve ( ) ( ) 130 0.5 500 200 500 130 0.5 0.5 500 200 500 ' 0.5 330 1000 0.5 d d d S Y C G Y Y T r G I r Y Y T r G r IS Y r G T = - - = - + - - - = = - - - + + - = - = - + -

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In the short-run there is no change in P . As before, use IS to replace r in the LM to get the AD curve, but now we can solve for Y . ( ) 600 6 1320 100 5 . 0 100 330 5 . 0 330 5 . 0 5 . 0 330 5 . 0 1000 5 . 0 = + - + = + - + = + - - + = + = P M T G Y P M Y T G Y P M r Y Now we can solve for the short-run equilibrium values for the rest of the endogenous variables ( ) ( ) 160 08 . 0 500 200 500 200 340 08 . 0 500 100 600 5 . 0 130 500 5 . 0 130 08 . 0 1000 80 1000 600 5 . 0 6 1320 1000 5 . 0 = - = - = = - - + = - - + = = = - = - = r I r T Y C r r r Y P M d d In the long-run, the price level will change and output returns to the full-employment level so we must re-solve ( ) ( ) LM P M r Y r Y P M IS T G r Y r G r T Y Y r I G r T Y Y G C Y S d d d + = - = - + - = - = - + + - - - = = - - - + - = - - = 1000 5 . 0 1000 5 . 0 5 . 0 1000 330 5 . 0 500 200 500 5 . 0 5 . 0 130 500 200 500 5 . 0 130 Use IS to replace r in the LM to get the AD curve. ( ) P M T G Y P M Y T G Y P M r Y + - + = + - - + = + = 5 . 0 330 5 . 0 5 . 0 330 5 . 0 1000 5 . 0
Use the fact that in equilibrium 500 = = Y Y to solve for the endogenous variables. ( ) ( ) 135 13 . 0 500 200 500 200 265 13 . 0 500 100 500 5 . 0 130 500 5 . 0 130 13 . 0 1000 130 1000 500 5 . 0 11 1320 1000 5 . 0 11 120 1320 1320 380 500 1320 100 5 . 0 100 330 500 5 . 0 330 = - = - = = - - + = - - + = = = - = - = = = + = + - + = + - + = r I r T Y C r r r Y P M P P P P M T G Y d d P LRAS 11 SRAS’ 6 SRAS AD’ AD 500 600 Y

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2. Numerical Problem #3 from Abel and Bernanke Chapter 11, found on page 433. ( ) ( ) IS T G r Y r G r T Y Y r I G r T Y Y G C Y S d d d - + - = - = - + + - - - = = - - - + - = - - = 8 . 0 1000 1000 2 . 0 500 400 500 8 . 0 8 . 0 600 500 400 500 8 . 0 600 If in fact we are in equilibrium at 8000 = = Y Y this would require us to be on the IS curve, giving us 4 . 0 1000 400 1000 1200 1600 1000 8 . 0 1000 1000 1000 8000 2 . 0 5000 6000 1000 1200 1000 8 . 0 1000 1000 1000 2 . 0 8 . 0 1000 1000 2 . 0 - = - = - = - + - = - = - = - + - = - + - = r r r r Y r r Y T G r Y A negative real interest rate is not possible (see the graph below.) The LM curve, shown in red below, cannot go negative, if it could (the hypothetical dashed portion), the intersection would be at the negative interest rate. Notice that this calculation is independent of the money supply and the price level. No matter what values they take on, we can never get to full employment output.
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