Question

Question 4. Using your knowledge of IS-LM, solve the following: 8

12

1+r 1+r

1. (a) If the consumption function is given by C = 100 + 0.6(Y − T ), planned investment is given by 1000 − 100r, G is equal to 100, and T is equal to 100. Solve for the IS equation (hint:Y as a function of r). The economy is a closed economy.

2. (b) If the money supply is equal to 2000 and real money demand, (M/P)d is given by Y −150r, solve for the LM curve (hint: again, Y as a function of r). Also assume that P = 1.

3. (c) Using the IS and LM equations, solve for equilibrium income (Y ) and interest rate (r) in this economy.

Answer 1

a) IS equation is given as

Y = C + I + G

Y = 100 + 0.6(Y -T) + 1000 - 100r + 100

Y = 1200 + 0.6(Y - 100) - 100r

Y = 1200 + 0.6Y - 60 - 100r  

Y = 1140 + 0.6Y - 100r

Y - 0.6Y = 1140 - 100r

0.4Y = 1140 - 100r  

Y = 2850 - 250r  

b) LM equation is given as

(M/P)^d = M/P  

Y - 150r = 2000/1

Y = 2000 + 150r

c) In equilibrium Y_IS = Y_LM

2850 - 250r = 2000 + 150r  

2850 - 2000 = 150r + 250r

850 = 400r

r = 850/400

r = 2.125

Y = 2000 + 150r

Y = 2000 + 150(2.125)

Y = 2000 + 318.75

Y = 2318.75