a. The consumption function is C = 1.5 + 0.75( Y – T ). What is the marginal pro

Question

a. The consumption function is C = 1.5 + 0.75(Y – T). What is the marginal propensity to

consume, MPC? What is the marginal propensity to save, MPS?

b. The trade balance is TB = 5(1 – [1 / E]) – 0.25(Y – 8). What is the marginal propensity to consume foreign goods, MPCF? What is the marginal propensity to consume home goods, MPCH?

c. The investment function is I = 2 – 10i. What is investment when the interest rate i is equal to 0.10 = 10%?

d. Assume government spending is G. Add up the four components of demand and write down the expression for D.

e. Assume forex market equilibrium is given by i = ([1 / E] – 1) + 0.10 where the two Foreign return terms on the right are expected depreciation and the Foreign interest rate. What is the foreign interest rate? What is the expected future exchange rate?

f. (No. 8). Continuing the last question, and solving for the IS curve, obtain an expression for Y in terms of i, G, and T (eliminate E).

Explanation / Answer

a)

Consider the given problem, here the consumption function is given by, “C=1.5+0.75*(Y-T), so here MPC be the additional consumption if “Y” increases by 1 unit, => dC/dY=0.75, so “MPC=0.75”, and “MPS=1.-MPC=0.25”.

b).

So, here “TB=5*(1 – (1/E)) – 0.25*(Y- 8). So here MPCF is the additional consumption when Y increases by 1 unit, mathematically, MPCF=(-)(dT/dY),=> MPCF=0.25.

So, here the MPCH is the difference between “MPC – MPCF =0.75 – 0.25 = 0.5”.

c).

let’s assume that the “Investment function” is given by “I=2 – 10*I”, so if i=10%=0.1, then

I=2-0.1*10 = 2-1=1.

So, the investment is I=1.

d).

so, there are 4 component, so the “expenditure function” is given by “D=C+I+G+TB”.

D=1.5 + 0.75*(Y-T) + (2 – 10*i) + G + 5*[ 1 - (1/E) ] – 0.25*(Y – 8),

=> D = 1.5 + 0.75*Y – 0.75*T + 2 – 10*i + G + 5 – 5*(1/E) – 0.25*Y + 0.25*8.

=> D = (1.5 – 0.75*T + 2 + G +5 – 5*(1/E) + 0.25*8] + 0.75*Y – 10*i – 0.25*Y.

=> D = [ 10.5 -0.75*T +G – 5*(1/E) ] + 0.5*Y – 10*i.

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