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Assume that the following equations summarize the structure of an economy.

C C0.8(YT); C 700-15r T 200+0.2Y; (M P) 0.1Y-10r; M P 440; I = 600-25r; G 1,000; NX 100 0.04Y

Answer the following questions:

            (a) What is the equation of the IS curve?

            (b) What is the equation of the LM curve?

            (c) What is the equilibrium real output?

            (d) What is the equilibrium interest rate?

            (e) What is the level of saving at equilibrium?

  1. What is the level of planned investment at equilibrium?
  2. Determine whether leakages equal injections at equilibrium.
  3. Assume that r = 4 and Y = 5000. Is there an excess demand for money or an excess supply of money? How much? Is there unplanned inventory change? If so, what is its value?
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Answer #1

a) IS curve

C = Ca + 0.8(Y - T)

Ca = 700 - 15r

C = 700 +0.8(Y - T) - 15r

Y = C + I + G + NX

= 700 +0.8(Y - T) - 15r + 600 - 25r + 1000 + 100 - 0.04Y

= 2400 + 0.8(Y - 200 - 0.2Y) - 40r - 0.04Y

= 2400 + 0.8(0.8Y - 200) - 40r - 0.04Y

= 2400 + 0.64Y - 160 - 40r - 0.04Y

= 2240 + 0.60Y - 40r

Y - 0.6Y = 2240 - 40r

0.4Y = 2240 - 40r

Y = 5600 - 100r

or

100r = 5600 - Y

r = 56 - Y/100

b) LM curve is given by

(M/P)d = Ms/P

0.1Y - 10r = 440

0.1Y = 440 + 10r

Y = 4400 + 100r

or

Y - 4400 = 100r

r = Y/100 - 44

C) In equilibrium

rLM   = rIS

Y/100 - 44 = 56 - Y/100

Y/100 + Y/100 = 56 + 44

2Y/100 = 100

Y/50 = 100

Y = 5000

d)

r = Y/100 - 44

= 5000/100 - 44

= 50 - 44

= 6  

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