Question

In: Economics

IS-LM Model (Closed Economy) The following equations describe a small open economy. [Figures are in millions...

IS-LM Model (Closed Economy)

The following equations describe a small open economy.

[Figures are in millions of dollars; interest rate (i) is in percent]. Assume that the price level is fixed.

Goods Market

C = 250 + 0.8YD

YD = Y + TR – T

T = 100 + 0.25Y

I = 300 – 50i

G = 350; TR = 150

Money Market

L = 0.25Y – 62.5i

Ms/P = 250

Goods market equilibrium condition: Y = C + I + G + X-M

Money market equilibrium condition: L = Ms/P

a) What is the equation that describes the IS curve (Y_IS)?

b) What is the equation describing the LM curve (Y_LM)?

c) What are the equilibrium levels of income (Y_o) and interest rate (i_o)

Expert Solution

(a)

In goods market equilibrium, Y = C + I + G + X - M

Y = 250 + 0.8[Y + 150 - (100 + 0.25Y)] + 300 - 50i + 350 [Since X = M = 0]

Y = 900 + 0.8(Y + 150 - 100 - 0.25Y) - 50i

Y = 900 + 0.8(0.75Y + 50) - 50i

Y = 900 + 0.6Y + 40 - 50i

0.4Y = 940 - 50i

Y = 2350 - 125i..........(IS equation)

(b)

In money market equilibrium, L = Ms/P

0.25Y – 62.5i = 250

0.25Y = 250 + 62.5i

Y = 1000 + 250i.........(LM equation)

(c)

In equilibrium, Y_IS = Y_LM.

2350 - 125i = 1000 + 250i

375i = 1350

i = 3.6

Y = 1000 + (250 x 3.6) = 1000 + 900 = 1900

Rahul Sunny answered 2 years ago

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