Chapter 10 Solution

# From is lm 4250 125i 2000 250i 2250 375i i 6 y 4250

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From IS = LM ==> 4,250 - 125i = 2,000 + 250i ==> 2,250 = 375I ==> i = 6 ==> Y = 4,250 - 125*6 = 4,250 - 750 ==> Y = 3,500 Check: Y = 2,000 + 250*6 = 2,000 + 1,500 = 3,500 i 125 IS LM 6 0 2,000 3,500 4,250 Y

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150 2.a. As we have seen in 1.a., the value of the expenditure multiplier is α = 2.5. This multiplier α is derived in the same way as in Chapter 9. But now intended spending also depends on the interest rate, so we no longer have Y = α A o , but rather Y = α (A o - bi) = (1/[1 - c + ct])(A o - bi) ==> Y = (2.5)(1,700 - 50i) = 4,250 - 125i. 2.b.This can be answered most easily with a numerical example. Assume that government purchases increase by G = 300. The IS-curve shifts parallel to the right by ==> IS = (2.5)(300) = 750. Therefore IS': Y = 5,000 - 125i From IS' = LM ==> 5,000 - 125i = 2,000 + 250i ==> 375i = 3,000 ==> i = 8 ==> Y = 2,000 + 250*8 ==> Y = 4,000 ==> Y = 500 When interest rates are assumed to be constant, the size of the multiplier is equal to α = 2.5, that is, ( Y)/( G) = 750/300 = 2.5. But when interest rates are allowed to vary, the size of the multiplier is reduced to α 1 = ( Y)/( G) = 500/300 = 1.67. 2.c. Since an increase in government purchases by G = 300 causes a change in the interest rate of 2 percentage points, government spending has to change by G = 150 to increase the interest rate by 1 percentage point. 2.d. The simple multiplier α in 2.a. shows the magnitude of the horizontal shift in the IS-curve, given a change in autonomous spending by one unit. But an increase in income increases money demand and the interest rate. The increase in the interest rate crowds out some investment spending and this has a dampening effect on income. The multiplier effect in 2.b. is therefore smaller than the multiplier effect in 2.a. 3.a. An increase in the income tax rate (t) will reduce the size of the expenditure multiplier ( α ). But as the multiplier becomes smaller, the IS-curve becomes steeper. As we can see from the equation for the IS-curve, this is not a parallel shift but rather a rotation around the vertical intercept. Y = α (A o - bi) = [1/(1 - c + ct)](A o - bi) ==> i = (1/b)A o - ( α /b)Y = (1/b)A o - (1/b)[1 - c + ct]Y 3.b. If the IS-curve shifts to the left and becomes steeper, the equilibrium income level will decrease. A higher tax rate reduces private spending and this will lower national income. 3.c. When the income tax rate is increased, the equilibrium interest rate will also decrease. The adjustment to the new equilibrium can be expressed as follows (see graph on the next page): t up ==> C down ==> Y down ==> m d down ==> i down ==> I up ==> Y up. Effect: Y and i
151 IS 1 i IS o LM i 1 i 2 0 Y 2 Y 1 Y 4.a. If money demand is less interest sensitive, then the LM-curve is steeper and monetary policy changes affect equilibrium income to a larger degree. If money supply is assumed to be fixed, the adjustment to a new equilibrium in the money sector has to come solely through changes in money demand. If money demand is less interest sensitive, any increase in money supply requires a larger increase in income and a larger decrease in the interest rate in order to bring the money sector into a new equilibrium.

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