Refer to the first equilibrium income you calculated in problem 4. Now suppose t
ID: 1152728 • Letter: R
Question
Refer to the first equilibrium income you calculated in problem 4. Now suppose that the intercept of the net tax function ( t 0) changes from -50 to -40. Find the new level of equilibrium income
This is ans 4:
The components of aggregate demand (AD) are as follows: AD= C+I+G+NX where C: Consumption, I: Investment, G: Government Spending and NX: Net Exports. This example is that of a closed economy which means that there is no ‘net exports’ involved.
From the given information, we know that the aggregate consumption function is given by C = 25 + 0.8YD where YD is disposable income (income left after payment of taxes) given by (Y-T). The intended investment is 75 and the level of government spending ( G ) was 100. Net taxes ( T ) are initially given by the tax function T = -50 + 0.30Y
Here Y is the income and output where Y=C+I+G+NX.
Thus, Y = 25 + 0.8YD + 75 + 100
Or Y = 25 + 0.8(Y+50-0.30Y) + 175
Or Y = 200 + 0.8Y + 40 – 0.24Y
Or Y- 0.56Y = 240
Or Y = 545.45
Thus the equilibrium income when tax rate = 0.30 is Y = 545.45 units.
When the tax rate changes from 0.30 to 0.25, the tax equation becomes T = -50 + 0.25Y
Thus,
Y = 25 + 0.8YD + 75 + 100
Or Y = 25 + 0.8(Y+50-0.25Y) + 175
Or Y = 200 + 0.8Y + 40 – 0.2Y
Or Y- 0.6Y = 240
Or Y = 600
Thus the equilibrium income when tax rate = 0.30 is Y = 600 units. The income/output Y rises because a fall in tax rate raises the disposable income and in turn raises consumption thereby stimulating Y.
The formula of autonomous expenditure multiplier is given by:
1/{1- MPC* (1-t)} where MPC is the marginal propensity to consume and t is the tax rate.
The MPC is given by the value 0.8 which is the slope of the consumption function
Therefore autonomous expenditure multiplier before tax cut when tax rate is 0.30 = 1/ {1- 0.8* (1-0.3)} = 2.273
Similarly, autonomous expenditure multiplier after tax cut when tax rate is 0.25 = 1/ {1- 0.8* (1-0.25)} = 2.50.
Explanation / Answer
New tax function: T = - 40 + 0.3Y
Disposable income (YD) = Y - T = Y - (- 40 + 0.3Y) = Y + 40 - 0.3Y = 0.7Y + 40
Consumption function: C = 25 + 0.8YD = 25 + 0.8 x (0.7Y + 40) = 25 + 0.56Y + 32 = 57 + 0.56Y
Therefore, in new equilibrium,
Y = C + I + G + NX
Y = 57 + 0.56Y + 75 + 100 (NX not being given, is assumed to be 0).
(1 - 0.56)Y = 232
0.44Y = 232
Y = 527.27