Question

Consider IS-LM model. Let the money demand function be left parenthesis M over P right parenthesis to the power of d equals 60 minus 20 r plus 4 Y, the consumption function be C equals 12 plus 0.8 left parenthesis Y minus T right parenthesis and the investment function be I equals 30 minus 2 rI where r is the real interest rate in %. Let T denote taxes, G denote government purchases, P denote the price level and M to the power of S denote the money supply. Calculate the following (Round up to TWO decimal places if needed. Enter only numbers)

(1) Assume that T = 20, G = 10, P = 3 and = 300.

(a) Calculate the equilibrium real interest rate r

(b) Calculate income Y

(c)  Calculate consumption C  

(d)  Calculate investment I

(2) Suppose the government decreases G from 10 to 6. What will be the new equilibrium level of Y and r?

(a) r =

(b) Y=

(3) Suppose the new level of money supply is = 240 (while G stays at 10), what is the new equilibrium level of Y and r?  

(a) r =

(b) Y=

Answer 1

a, b).

Consider the given problem here the money supply is “Ms=300” and the price level is “P=3”, => the real money balance is “M/P = 300/3 = 100”. The money demand function is given below.

=> (M/P)d = 60 – 20*r + 4*Y, at the equilibrium the demand must be equal to supply.

=> 60 – 20*r + 4*Y = 100, => 4*Y – 20*r = 40, be the equation of LM curve.

The IS shows the goods market equilibrium, => the goods market equilibrium condition are given below.

=> Y = C + I + G, => Y = 12 + 0.8*(Y-T) + 30 – 2*r + 10, => Y = 52 + 0.8*Y – 0.8*T – 2*r.

=> 0.2*Y = 52 – 0.8*20 – 2*r, => 0.2*Y = 36 – 2*r, be the IS equation.

The LM equation is “4*Y – 20*r = 40”, => 20*r = 4*Y - 40, => 2*r = 0.4*Y – 4.

Now, substituting the above condition on the IS curve we get the following condition.

=> 0.2*Y = 36 – 2*r = 36 – [0.4*Y – 4] = 36 – 0.4*Y + 4 = 40 – 0.4*Y.

=> 0.2*Y = 40 – 0.4*Y, => Y = 40/0.6 = 66.67.

From the LM equation we got “2*r = 0.4*Y – 4 = 0.4*66.67 – 4 = 22.67”, => r = 22.67/2 = 11.33, => r = 11.33%.

So, the equilibrium interest rate is “r=11.33%” and the income is “Y=66.67”.

c, d).

The consumption is “C = 12 + 0.8*(Y-T) = 12 + 0.8*(66.67-20) = 49.34, => C = 49.34.

The Investment is “I = 30 – 2*r = 30 – 2*11.33 = 7.34”, => I = 7.34.