Consider the following IS/LM model of a closed economy; The interest rate (r) an

Question

Consider the following IS/LM model of a closed economy;

The interest rate (r) and real income (Y) are endogenously determined variables in this economy. We
continue to ignore the FE line and so treat the price level (.P) as exogenously determined and fixed.

(a) Derive equations of IS and LM. Explain each step in your derivations. [10 marks]

(b) Find the equilibrium values of r and Y. Explain each step in your derivations. [10 marks]

(c) ) Derive the numerical value of the fiscal policy multiplier (deltaY/delta G). Describe each step in your
derivation. [10 marks]

Explanation / Answer

IS equation

Investment = saving

so Y = C + I + G = 100 + 0.6(Y-0.25Y) + 100 - 55r + 240 = 440 - 55r + 0.45Y

so r = (440 - .55Y) / 55 = 8 - .01Y

LM equation

(M/P)d = (M/P)s

500 + 0.2Y - 25r = 520

r = (0.2Y - 20) / 25 = 0.008Y - 0.8

b) At equilibrium IS=LM

8 - 0.1Y = 0.008Y - 0.8

0.108Y = 8.8

so Y=81.5

r = 0.15

C) Here we see that G is not a function of Y or anyrging else, so any change in G will cause the exact same change in Y i,e, if G is increased by 100 then Y will also increase by 100 so delta Y = delta G. Therefore fiscal policy multiplier delta Y / delta G = 1

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