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.

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

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


(d) Define the government budget deficit (D) as the difference between government expenditure and tax
revenue. Thus D = G - T, or using equation (3) to substitute for T we find;

(10) D = G-0.25Y

What is the size of the government budget deficit in the equilibrium you defined in part (b )?

(e) ) Use equation (10) to derive an expression for the "deficit multiplier" (delta D/delta.G). Use this
expression to show that despite the fact that an increase in government expenditures increases tax
revenues, an increase in government expenditures makes the deficit larger.

6 2 (2) = 100 + 0.6(Y-T) (3) T= 0.25Y (4) = 100-55r (5) G=240 (6) AE- Y (7) (M/pf = 500 + 0.2Y-25r (8) (M/P)',-520 5

Explanation / Answer

(a)

(i) IS Curve equation in a closed economy is:

Y (AE) = C + I + G

Y = 100 + 0.6(Y - T) + 100 - 55r + 240

= 440 + 0.6(Y - 0.25Y) - 55r [Since T = 0.25Y]

Y = 440 + 0.6 x 0.75Y - 55r

Y = 440 + 0.45Y - 55r

(1 - 0.45)Y = 440 - 55r

0.55Y = 440 - 55r

Y = 800 - 100r ......(1) [Equation of IS]

(ii) Equation of LM states that

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

500 + 0.2Y - 25r = 520

0.2Y = 20 + 25r

Y = 100 + 125r ....... (2) [LM Curve]

(b)

The economy is in equilibrium when IS = LM, and we derive equilibrium r & y by equating (1) with (2) in part (a):

800 - 100r = 100 + 125r

225r = 700

r = 700/225 = 3.11

Y = 100 + 125r = 100 + (125 x 3.11) = 100 + 388.75 = 488.75

(c)

If marginal propensity to consume (MPC) is C, then

Government expenditure multiplier = 1 / (1 - C)

Here, C = 0.6 [From consumption function]

So, Multiplier = 1 / (1 - 0.6) = 1 / 0.4 = 2.5

(d)

Deficit, D = G - 0.25Y

Since Y = 488.75 & G = 240,

D = 240 - (0.25 x 488.75) = 240 - 122.1875 = 117.8125

Since D > 0, there is a budget surplus.

NOTE: Out of 5 sub-parts the first 4 are answered in full.

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