Econ 162B A0 A1 Fall 2011 ANSWER KEY PROBLEM SET NUMBER EIGHT 1 The consumption function is C Kenny Christianson due November 18 Y C C The saving function is 200 C 200 0 9Yd S 200 0 1Yd 0 200 0 1Y 200 0 1Y Y 200 0 9Y 0 1Y 200 Y 2000 The level of income where saving 0 or Yd C is assuming T 0 S 2000 Yd Y 2000 or setting Y C S Yd 2000 200 2 First from the table find aggregate expenditures AE C I G X M Y C S I G X M T AE Yd 0 100 200 300 400 500 600 700 800 900 1000 20 100 180 260 340 420 500 580 660 740 820 120 100 80 60 40 20 0 20 40 60 80 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 20 20 20 20 20 20 20 20 20 20 20 100 120 100 0 100 200 100 100 280 200 100 360 300 100 440 400 100 520 500 100 600 600 100 680 700 100 760 800 100 840 900 100 920 a The MPC C Y 80 100 0 8 The MPS S Y 20 100 0 2 b The consumption function is The saving function is C 100 0 8Yd S 100 0 2Yd c The equilibrium level of GDP is 600 where Y AE Econ 162B A0 A1 Fall 2011 Answer Key 8 2 3 In order to find the equilibrium GDP plug the information into the first equation a AE C I G X M AE 800 75Y 400 200 200 so AE 1600 75Y Y AE is the equilibrium condition so Y 1600 75Y Y 75Y 1600 Y 1 75 1600 Y 1 1 75 x 1600 4 x 1600 6400 spending multiplier equilibrium GDP c spending multiplier 1 1 MPC 1 1 75 4 c d d C 800 0 75 6400 5600 S Yd C 6400 5600 800 e Y spending multiplier x G Y 4 x 100 400 so Y 6400 400 6800 or plug new G into original equation Y 800 75Y 400 300 200 so AE 1700 75Y Y 1700 75Y 25Y 1700 Y 1 25 x 1700 6800 b Graphically Y AE AE AE 6800 AE 6400 1700 1600 6400 6800 Y Econ 162B A0 A1 Fall 2011 Answer Key 8 3 4 If imports are induced substitute the import function for M in the AE equation from question 3 a AE 800 75Y 400 200 300 100 15Y AE 800 75Y 400 200 300 100 15Y AE 1600 75Y 15Y so AE 1600 0 6Y If Y AE then Y 1600 75Y 15Y Y 75Y 15Y 1600 Y 1 75 15 1600 Y 1 1 75 15 x 1600 1 4 x 1600 2 5 x 1600 4000 multiplier 1 MPS MPIM equilibrium GDP b The spending multiplier is 1 MPS MPIM 2 5 The multiplier is smaller than in 2 because imports are induced c X M 300 100 15Y 300 100 15 4000 300 700 400 5 If T 200 first find the AE function then set Y AE AE 800 75 Y 200 400 200 200 AE 800 75Y 75 200 400 200 200 so AE 1450 0 75Y Set Y AE Y 800 75 Y 200 400 200 200 Y 800 75Y 75 200 400 200 200 Y 75Y 75 200 1600 Y 75Y 75 200 1600 Y 1 75 75 200 1600 Y 75 1 75 200 1 1 75 1600 tax multiplier spending multiplier Y 3 200 4 1600 5800 tax multiplier MPC 1 MPC 75 1 75 3 spending multiplier 1 1 MPC 1 1 75 4 Econ 162B A0 A1 Fall 2011 Answer Key 8 4 6 This is a trick question Since the MPC is equal to one then the multiplier is equal to 1 1 1 which is undefined Any small change in spending will lead to an infinite increase in GDP The model does not converge to an equilibrium Graphically the AE curve is parallel to the 45 degree line so no equilibrium exists Graphically AE C C Y C 700 400 Y
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