Exercise 3

Exercise 3
What happens to steady values of output when personal income tax changes?
In the steady state G = T .
G = tWN and T = tY where t is the personal income tax rate,W is wages and N is the constant population.

This results in the following identity in the steady state:
Y = G/t

In the steady state national income will increase when the level of personal income taxation is reduced. This will reduce the value of the denominator in the formula above and thereby increase national income. This is not a wise policy for a government to adopt in the long run because in times of crisis the government will face budget deficits.
Similarly, national income will decrease when the level of personal taxation is increased. This is because higher taxes will reduce consumers spending and in turn national income.
In the steady state:

Y = G/t = tWN/t

When personal income tax changes, wages must change in order for income to change. If personal income tax decreases ,then wages must increase in order for national income to increase as the population is assumed to be constant.