A lump-sum tax is a tax that is simply levied on an economy as a flat amount. This amount does

What will be an ideal response?

not change with the level of income. Suppose that a lump-sum tax is levied in an economy with
a government (but no foreign sector). Because consumption in this economy is C = C× + mpc Yd
while disposable income is Yd = Y - T× + TR, we can write the consumption function a
C== ×C + mpc (Y - ×T + TR)
Thus aggregate demand in this economy can be expressed as:
AD = C + II + G
= ×C + mpc (Y - ×T + TR) + II + G
= ( ×C - mpc ×T + mpc TR + II + G) + mpc Y
The last rearrangement shows that the AD curve has an intercept equal to the term in
parentheses and a slope equal to the marginal propensity to consume. Changes in any of the
variable in parentheses, by changing the intercept, shift the curve upward or downward in
a parallel manner.
By substituting this into the equation for the equilibrium condition, Y = AD, we can derive
an expression for equilibrium income in terms of all the other variables in the model:
Y = (×C -mpc ×T + mpc TR + II + G) + mpc Y
Y - mpc Y = ×C - mpc ×T + mpc TR + II + G
(1 - mpc)Y = ×C - mpc ×T + mpcTR + II + G
Y = 1 (×C - mpc ×T + mpc TR + II + G)