Suppose that Cascadias economy is described by the following

Suppose that Cascadia\'s economy is described by the following equations: C-200+.75YD 1-100 Z-C+I+G with YD=Y-T G-200 T= 100 where C is consumption, Yo is disposable income, Y is output (income), T is tax, I is autonomous investment, G is government spending, and Z is aggregate spending (demand)

Solution

The information provided in the question is:

C = 200 + 0.75*(Y – 100), I = 100, G = 200, Z = C + I + G.

Currently the equilibrium level of income is

Y = 200 + 0.75*(Y – 100) + 100 + 200

Y = 425 – 0.75Y

Y* = 1700.

a) Government spending multiplier is 1/1 – MPC = 1/1 – 0.75 = 4. Hence we have mg = 4

b) When G rises by 25, income rises by mg x change in G = 4*25 = $100. New income is $1800. Change in income is $100 and new income is $1800.

c) New consumption is 200 + 0.75*(1800 – 100) = $1475 and old consumption is 200 + 0.75*(1700 – 100) = $1400. Hence change in consumption is $75.

d) Budget surplus / deficit = taxes – spending = T – G = 100 – 225 = -$125 (budget deficit)

e) A flat tax gives a multiplier value of 1/1 – MPC while a proportional tax gives a multiplier value of 1/1 – MPC(1- t). Here the proportional tax rate increases the multiplier value and so a proportional tax rate amplifies economic fluctuation.