Answer to Question #205564 in Macroeconomics for Akash

Question

Q) Suppose there are two groups of people in an economy, with their respective consumption function.

                        C_A=100+0.5Y_A

                        C_B=150+0.75Y_B

   planned investment 200.Where C_i and Y_i  are respectively consumption and income level

 for the ith group (for all i=A,B). Suppose each group gets 50% of total GDP in the economy.

Determine the equilibrium level of income. Considering the equilibrium income as the initial income, a lumpsum tax T is imposed on Group A and the same amount is given as a transfer to Group B.

 Now determine planned consumption, planned savings , planned aggregate Demand and the Actual Investment as the initial level of income

Answer 1

(a) Determination of equilibrium level of income

Y_i = AE = C_i + I

C_i = C_A + C_B = 100+ 0.5Y_A + 150 + 0.75Y_B

But since each receive 50% of GDP, Y_A = Y_B

Y_i = AE = 100 + 0.5Y + 150 + 0.75Y + 200 = 450 + 1.25Y

(b) Determination of;

i) Planned consumption

With introduction of lump-sum tax

C_A = 100 + 0.5 (Y_Ad) = 100 + 0.5 (Y-T)

C_B = 150 + 0.75 (Y_B+T)

ii) Planned Savings

For group A, Planned comsumption = 100 + 0.5(Y_A d)

MPC - 0.5, but MPS + MPC = 1

$\therefore$ MPS = 1 - 0.5 = 0.5

So planned savings for group B will be 0.5(Y_A-T).

For group B, planned consumption = 150 + 0.75(Y_B + T)

MPC = 0.75, but MPS + MPS = 1

$\therefore$ MPS = 1 - 0.75 = 0.25

So planned savings for group B = 0.25(Y_B + T)\

Aggregate Planned Savings = Planned savings for A + Planned savings for B

= 0.5(Y_A -T) + 0.25(Y_B+T) = 0.5Y_A - 0.5T + 0.25Y_B + 0.25T = 0.5Y_A + 0.25Y_B - 0.5T+0.25T

= 0.5Y_A + 0.25Y_B -0.25T

iii) Planned AD = Planned Aggregate consumption + Planned Investment

= Planned C_A + Planned C_B + Planned Investment

= 100 + 0.5 (Y_A -T) + 150 + 0.75(Y_B + T) + 200

= 450 + 0.5Y_A - 0.5T + 0.75Y_B + 0.75T

= 450 + 0.5Y_A +0.75Y_B + 0.25T

iv) At equilibrium, Actual investment (I) = Planned Investment (Ip) = 200