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Intermediate Economics B

Problem Set 4

1.  Consider an open economy characterised by the equations below

C   =   c0 + cl (Y − T)

I   =   d0 + dl Y

IM   =   ml Y

X   =   xl Y*

The parameters ml  and xl  are the propensities to import and export. Assume that the real exchange rate is fixed at a value of 1 and treat foreign income, Y* , as fixed. Also, assume that taxes are fixed and that government purchases are exogenous (i.e. decided by the government).  We explore the effectiveness of changes in G under alternative assumptions about the propensity to import.

a) Write the equilibrium condition in the market for domestic goods and solve for Y.

b)  Suppose government purchases increase by one unit.  What is the effect on output? (Assume that 0 < ml  < cl + < 1. Explain why.)

c) How do net exports change when government purchases increase by one unit?


Now consider two economies, one with ml  = 0.5 and the other with ml  = 0.1. Each economy is characterised by (cl + dl ) = 0.6.

d)  Suppose one of the economies is much larger than the other. Which economy do you expect to have the larger value of ml ? Explain.

e)  Calculate your answers to parts (b) and (c) for each economy by substituting the appropriate parameter values.

f) In which economy will fiscal policy have a larger effect on output?  In which economy will fiscal policy have a larger effect on net exports?

2. In chapter 3, we have assumed that the fiscal policy variables G and T are indepen- dent of the level of income. In the real world, however, this is not the case. Taxes typically depend on the level of income and so tend to be higher when income is higher. In this problem, we examine how this automatic response of taxes can help

reduce the impact of changes in autonomous spending on output. Consider the following behavioural equations:

C = c0 + cl Y

T = t0 + tl Y

YD  = Y − T

G and I are both constant. Assume that tl  is between 0 and 1.

a)  Solve for equilibrium output.

b) What is the multiplier?  Does the economy respond more to changes in au- tonomous spending when tl  is 0 or when tl  is positive? Explain.

c) Why is fiscal policy in this case called an automatic stabiliser?