In the two-period model suppose that the government reduces taxes by /\\t in the
ID: 1224691 • Letter: I
Question
In the two-period model suppose that the government reduces taxes by / in the current period for only N/2 consumers leaving taxes unchanged for the other N/2 consumers. In the future period, the government raises taxes by / (1 + r) on the N/2 consumers who did not receive a tax cut leaving taxes unchanged for the other N/2 consumers. (/ = change)
a. Show that this fiscal policy satisfies the government’s intertemporal budget constraint where G and G' are given.
b. What wealth effects, if any, do the two groups of consumers experience from these tax decreases and increases?
Explanation / Answer
A Budget constraint for a Two-period model is :
Y0= PC consumption at time period 0 + PC consumption at time period 1………………………………………………(1)
In our case at time period 0:
G or PC consumption at time period 0 :
N/2(t-t) + N/2(t)………………………………………..(2)
Here N/2(t-t) is the tax revenues from N/2 of the people whose tax was changed by t
And N/2(t) is the tax revenue from the remaining population whose tax was not changed.
G’ or PC consumption at time period 1 :
N/2(t-t) + N/2(t+ t(1+r) )………………………… (3)
Here N/2(t-t): is the tax revenue generated from N/2 population as in time period 0
And N/2(t+ t(1+r) ) is the tax revenue from N/2 population for whom the tax was increased by / (1 + r)
Answer
Putting (2) and (3) in (1) we get
Where G: total government Income for time periods 0 and 1
Now
Note: income at time 1 converts to consumption 1 to 1, that is what it meant to assume that the nominal price is 1 both periods.
So
G+ G’= Government income translated to spending is=
N/2(t-t) + N/2(t) + N/2(t-t) + N/2(t+ t(1+r) )
Thus, fiscal policy satisfies the government’s intertemporal budget constraint as
b. For the first group for whom government reduces taxes by / in the current period there is an increase in the disposable income leading to an increase in the wealth in the long run if rates remain so.
For the second group i.e. N/2 consumers who did not receive a tax cut leaving taxes unchanged and now government raises taxes by / (1 + r) i the current period, witness a reduction i the disposable income and thus a decrease in wealth if the rates continue to be so.