1 4 .02 P r in c ip les of Ma cr oec onomic sProblem Set #3 - AnswersOctober 16, 20021 PART I. True, False, Uncertain1 Workers like inflation since it raises their wages.False: Workers only care about real wages (W/P) and not about the nominallevel of wages which presumably increases with inflation.2 Impro vements in health that increase the elderly populationtend to increase the unemployment rate.False: An increase in the amoun t of elderly in the population won’t increasethelaborforceandtheamountofpeoplelookingforjobs. Theagingprocesswo uld decrease the participation rate but need not imply an increase in theunemployment rate .3 If the government increases G without altering the supply ofmoney, the amount of money demanded in equilibrium variessince both Y and i change.False: An increase in G tends to expand the level of output and then theMd(Y,i)shiftsupinthefinancial market graph. Nevertheless, the amounton money demanded in equilibrium has to be equal to the supply of money,which did not change. To restore the equilibrium, the interest rate goes upcompensating the positive effect of the higher income in the money demand.In equilibrium, the amoun t of money demanded is exactly equal to the fixedsupply of money.4 A monetary con traction cannot affect the public budget since itis not a fiscal policy.False: A monetary contraction tends to increase the interest rate (it shifts theLM curve to the left). The demand for investment decreases and the equilibriumlevel of output is smaller. If part of the go vernment revenues were collected withproportional income tax, the total amount of public revenues will decrease andthe public budget will be affected.15 As in microeconomics, the AS curve is upward slopping becauseproducers sell more goods when the price is high.False: The AS curve is upward sloping because a higher output level isequivalent to a lower unemploy ment rate. A lower unemployment rate givesthe worker higher bargaining power in the wage setting process and the levelof prices increases on wage (with the same simplifying assumptions used in thebook, the level of prices is proportional to the wage).2 PART II. IS-LM modelSuppose the population in the economy is divided in to two groups.Although the two groups have equal amount of people, the richer one(Group A) gets 70% of total income and the poorer one (Group B)gets the remaining 30%. The economy is represented by the follo wingequations.Md=5Y − 120rMs= 10000I = 296 − 20i +0.1YCA= 120 + cA(YA− TA)CB=60+cB(YB− TB)G = 5001. Assuming cA= cB= 0.6 and TA= TB= 200,derivetheISandLMcurve and find the equilibrium level of output and interest rateand compute the fiscal budget. Use graphs and math.The resulting consumption equations are:CA= 120 + 0.6(0.7Y − 200)CB=60+0.6(0.3Y − 200)Replacing in the equilibrium conditions Ms= Mdand Y = CA+CB+I +G,the IS and LM curves can be derived:LM : i = −2503+124YIS : i = −.015Y +36.8202468i2000 2040 2060 2080 2100 2120 2140 2160 2180 2200YSolution is : {i =5.0,Y = 2120.0}Finally, the fiscal deficit is G − TA− TB= 100.2 The government wants to reduce the fiscal deficit, but it is wor-ried about the negative consequences such a policy might have onthe level of output. What combination of monetary and fiscalpolicies would you recommend to decrease the deficit withoutprovoking a recession? Explain graphically and give the intu-ition.A fiscal contraction (increase in taxes or decrease in government consump-tion) reduces the fiscal deficit but has negative effects on the level of output (shiftIS curve down). To mitigate the negative effect on output, the fiscal contrac-tion can be implemented together with a monetary expansion (shift LM curve tothe right). The monetary expansion promote investment through lower interestrates. Eventually, the increase in investment can compensate the decrease inthe public expenditure (or increase in taxes).02468i2060 2080 2100 2120 2140 2160 2180 2200Y3 Assume now cA=0.4andcB= 0.8. Derive the IS and LM curveand find the equilibrium level of output and interest rate. Usegraphs and math.There is a miscomputation in the above question. With cA=0.4andcB=0.8 the exercise leads to a negative interest rate. In this case3CA= 120 + 0.4(0.7Y − 200)CB=60+0.8(0.3Y − 200)Replacing in the equilibrium conditions Ms= Mdand Y = CA+CB+I +G,the IS and LM curves can be derived:LM : i = −2503+124YIS : i = −.019Y +36.8,Solution is: {i = −0.82418,Y = 1980}The right intuition of the excercise can be obtained using cA=0.5and cB=0.9. Inthiscase:The resulting consumption equations are:CA= 120 + 0.5(0.7Y − 200)CB=60+0.9(0.3Y − 200)Replacing in the equilibrium conditions Ms= Mdand Y = CA+CB+I +G,the IS and LM curves can be derived:LM : i = −2503+124YIS : i = −.014Y +34. 82345678i2060 2080 2100 2120 2140 2160 2180 2200Y,Solution is : {i =5,Y = 2122}4 Explain the effect on output, interest rate, demand of money,amount of money and investment of a public transfer to GroupB financed by an increase in the tax leveraged to Group A.The policy includes taxing the Group A to finance the transfer to Group B.Notice that a transfer is a negative tax. Then: ∆TA= −∆TB> 0.Sincethepropensity to consume is higher within the Group B, the autonomous spendingincreases in (0.8 − 0.4)∆TA-using the marginal propensity to consume cA=0.5 and cB=0.9, the autonomous spending increases in (0.9 − 0.5)∆TA-. Sothe IS curve shifts up and both the interest rate and level of income are higherin equilibrium.In extension: the increase in autonomous spending causes an increase inoutput, the demand of money tends to increase but since the supply of money4is fixed, the interest rate has to go up in order to reestablish the equilibriumin the money market. The overall effect on investment is ambiguous (higheroutput tends to increase it but higher in terest rate tends to decrease it).2345678i2060 2080 2100 2120 2140 2160 2180 2200Y5 Explain the effect on output and interest rate of a more equaldistribution of incomeIn this case, the slope of the total consumption with respect to incomeincreases: ∆C = ∆CA+ ∆CB=0.4∆YA+0.8 · ∆YB= −0.4 · ∆sh · Y +0.8 ·∆sh · Y =0.4 · ∆sh · Y(Using the marginal propensities to consume cA=0.5andcB=0.9,thesame answer is obtained:∆C = ∆CA+ ∆CB=0.5∆YA+0.9 · ∆YB= −0.5 · ∆sh · Y +0.9 · ∆sh · Y =0.4 · ∆sh · Y )where ∆sh is the change in income share.An increase in the multiplier results in a flatter IS
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