Question

6. Suppose the economy is characterized by the following behavioral equations: C = 1,500+.6YD I= 2.000 - 10,000 G= 2,000 T= 2.000 a. At an interest rate of 10%, solve for equilibrium income (Y). disposable income (Y). consumption (C), investment (1), private saving, and public saving. b. What is the marginal propensity to consume in this economy? c. Now suppose that instead of taxes being a fixed quantity, taxes vary with income (as in many countries like the United States) so that T = 1,000+.15Y. At an interest rate of 10%, solve for equilibrium income (Y), disposable income (YD), consumption (C), investment (D). private saving, and public saving d. What does this type of tax system do to the stability of the economy in this model? (Maybe try "shocking the economy in each model by a 100 rise or fall in investment...)

Answer 1

et us firest solve for the equilibrium and derive required expressions algebraically. equilabrium, ly=C+I+G). We are given C = 1500+0.6 YD = 1500 +0.6(y-7), Where You disposable income - Y-T, 1 = 2000 - 10000, G -2009, T-2000 → Y = 1500 +0.6 -0.6T+2000-10000 R + G = 3500 +0.6 -0.6T-10000rc + > 1-0.6 = 3500+ G-0.6T-10000 R => y = 3500 G-06T-10OGOR 0.4 0.4 => y=8750 + G-06T-1000R 0.4 - equilibrium at goock market مل 9 T=1000+0.15 y instead of T-2000, at equile bruum, Y=C+I+G > y = 1500+ 0.67 -0.6 (1000+Hs y) +2000-10000reta >> Y-1500 +0.64-600-0.09Y+2000-10000 S+0.69-600 -0.09 Y + 2000-1000016 +G - 2900 +0.51Y 2000-10000re +G → 1-0:51 - 2900-1000orc + >TY-5918.37+ G-10000 0.49 (a) Al re=10%, GET=2000, Y=8750+ 2000-0.66 222000, Y-3750+ 2000-0.6 (2000)- 10000 (1) 2000-1200-1000 J-S1o - 287507 0.4 0.4 > y=875072209) = 9750-500 > y=9250 N Measuces Value + 9+ - - = 820 -20 o = 250 8250 → C = 1500+0.67 > 1500 +0.616250) - 5250 6250 and I = 2000-10000r 22cee-10000 (0:1) = 2000-1000 - 1000 5250 1000 Private Saving - Yo-C = 6250-5250 = 1000 Private saring 1000 Publie saving - T-G - 2000-2000 - 0 public saving | O. 06) Marginal propensity to consume is defined as the chang in comsumption due to awit changes in income. Symbolically, MPC 4. Applyeng this to the above consumplean function, we get, MPC (1500+0.64-0.6T) = 06 . Hence, marginal propensity to consum=0:6 (c) When T = 1000+0.1ST, using equation , we can save for other measures y = 5918.37+ 2060-10000(0-1)541937+ 1000 = 7959.8 Measures Value 0:49 ->T=1600 +0.15Y -1000+193.98 - 2193.88. Y 7959.18 T 2193.88 >>Y-T = 795918-2193.88 - 5765-31 5765:31 >> C=1500+0.6% = 1566 +06(5765-31) -4959.18 4959.13 1000 1 - 2000 - 100 cer =1000 Private saving - Yo-C-5765.31-4959.19 2 806-12 Private savings 806.12 Public saving -7-G2193-88-2000-193.88 Publir saving 193.88 (4) Let us see the difference of the tax system by some comparative statics. Froom equation 0 = 95,e. a unit change in G increase y by 2.5 times. For example, af Gis increased by 1000, y would charteaux by 25x1600 - 2500. when to becomes function of y, from equation @ 20:40 - 2.04 - Hence an increase in G by 1000 increases y by 2.04×1000 = 2040.82 > Lower increase than previous case. This is happening because the multiplier effect gets reduced cohen taxis dependent on income. Multiplier = Pc and MP c = 0.6 in scenario 1, which fell to o.5l in scenario 2 G-e.wth to ty). Hence, the multiplierus m scenario 1 and 2 are 1-018 4-2.5 and, -tosis = 2.04 respectively and (multipliere) <cultiplier) Sun.1 0:49