Question

Assume the following information for the economy:

C = c₀ + c₁Yd, where Yd = (1-t)Y                            C = 200 + 0.75(1-.2)Y

I = I                                                                 I = 700

G = G                                                              G = 800

X = X                                                               X = 400

M = mY                                                          M = 0.1Y

Find the savings.

Answer 1

Assume the following information for the economy:

C = c₀ + c₁ Y_d, where Y_d = (1 – t) Y

Now, c₀ = 200, c₁ (MPC = Marginal Propensity to Consume) = 0.75, t = 0.2

So, C = c₀ + c₁ (1 – t) Y = 200 + 0.75 (1 – 0.2) Y

I = 700

G = 800

X = 400

M = m Y, M (MPI = Marginal Propensity to Import) = 0.1

So, M = 0.1 Y

For an economy, at equilibrium,

Y = C + I + G + X – M

Or, Y = 200 + 0.75 (1 – 0.2) Y + 700 + 800 + 400 – 0.1 Y

Or, Y + 0.15 Y + 0.1 Y = 200 + 0.75 + 700 + 800 + 400

Or, 1.25 Y = 2100.75

Or, Y^* = 210075/125 = 1680.6

So, Y^* = 1680.6

And, s (MPS = Marginal Propensity to Save) = 1 – MPC = 1 - c₁ = 1 – 0.75 = 0.25

So, s^* = 0.25

Now, at equilibrium, we know that,

Investment = Savings (Private Savings (S) + Public Savings (T – G))

Or, Savings (S + (T – G)) = 700

In the above economy, T = 0 and G = 800

So, Private Savings (S) = 700 – (0 – 800) = 700 + 800 = 1500

And, Public Savings (T – G) = 0 – 800 = (- 800) [It is borrowings]

So, Total Savings of the economy is 700 units.

Hope the explanation is clear to you. Thank you.