Question

Answer parts 1-4. Please show all steps and formulas used.

Chapter 10: Income and Spending Example Suppose we have a closed economy with government described by the following functions: C = 50+ 0.8Yd ī = 70 G = 200 TR = 100 TA= 50 1) Calculate the equilibrium level of income in this case? 2) What is the level of saving in equilibrium? 3) If, for some reason, output is at the level of 800, what would be the level of involuntary inventory accumulation? 4) What is the value of the multiplier here? 5) If TR increases by 50, what would be the effect on the equilibrium income? What is the new equilibrium level of income? 6) Suppose the economy switches to a proportional income tax system (TA=tY with t=0.25. What is the new equilibrium level of income? What is the level of saving in the economy? 7) What is the value of the multiplier in this case? 8) What would be the effect on the equilibrium income if there is a proportional income tax at the rate of 0.25 and TR increases by 50? 9) If G reduces to 100, what would be the effect on the equilibrium level of income (assume that TR is constant at the initial level and the government imposes proportional income taxes)? 10) Calculate the budget surplus in this new economy with t = 0.25 (use initial values of G and TR). 11) What would be the changes in the budget surplus calculated in the previous part when G reduces to 100? 12) If t increases to 0.5, what would be the effect on the equilibrium level of income? What is the new equilibrium level of income? 13) Calculate the budget surplus in this new economy with t = 0.5. 14) What would be the changes in the budget surplus calculated in the previous part when G increases to 400? 15) Suppose I increases to 120, what would be the effect on the equilibrium level of income (consider t = 0.5)?

Answer 1

(1)

In equilibrium, Y = C + I + G

Y = 50 + 0.8(Y + 100 - 50) + 70 + 200 [since Yd = Y + TR - TA]

Y = 320 + 0.8(Y + 50)

Y = 320 + 0.8Y + 40

0.2Y = 360

Y = 1800

(2)

C = 50 + 0.8(1800 + 50) = 50 + 0.8 x 1850 = 50 + 1480 = 1530

(3)

Involuntary inventory accumulation = 1800 - 800 = 1000

(4)

Multiplier = 1 / (1 - MPC) = 1 / (1 - 0.8) = 1 / 0.2 = 5