What impact will this have on the marginal propensity to consume and on the multiplier?

Suppose that we introduce government so that the key economic relationships are represented by the following equations:

GDP identity:

Y = C + I + G                     Equation 1

Consumption function: C = 20 + 0.7 (Y – T)                   Equation 2

Tax equation: T = tY                                    Equation 3

I = 80                                                              Equation 4

G = 50                                                            Equation 5

T = 35                                                             Equation 6

t = 0.2                                                             Equation 7

Where:

Y = National Income

C = Consumption Expenditure

I = Investment Expenditure

G = Government Final Consumption Expenditure

T = income tax

t = marginal tax rate

All variables are measured in millions of euro.

c. Determine the final expenditures and leakages from the above equations.

d. Use the above equations to find the equilibrium value of income (Y) and the value of the income multiplier.

e. Show that in this economy, savings is equal to investment.