Barro,Chapter8QuestionsCraig BurnsideEconomics302University of Virginia8.2If someone gives up a unit of consumption at date t,they gain P t dollars,which can beused to purchase bonds maturing at t+1that will pay P t(1+R)dollars.These additionaldollars,in turn,will allow the person to purchase P t(1+R)/P t+1=(1+R)/(1+π)=1+rextra units of consumption at time t+1.8.4(a)i.1+R=(1+r)(1+π)=1.04×1=1.04so that R=0.04,or4%.(a)ii.Ifπ=0.10,or10%,we can use the approximation,R≈r+π=0.04+0.1=0.14(or14%).On the other hand if we wanted an exactfigure we would need to compute1+R=(1+r)(1+π)=1.04×1.1=1.144,so that R=0.144or14.4%.(b)There would be excess demand.If R didn’t rise in proportion toπ,then the realinterest rate would be lower than the equilibrium real interest rate.So people want to borrowtoo much tofinance higher consumption,and output would be too low because labor supplywould be lower.8.8The answer here depends on how you define revenue.If you define it in dollar termsthen the answer is yes.The government can always dump as much money into the economyas it wants,and its revenue is M t−M t−1,so the more money it pours in the more revenue it gets.But if you ask the question in terms of the purchasing power of the government’srevenue then the answer is no.Notice that the purchasing power of the government’s money isM t−M t−1P t.Take the example where Y and r and the money growth rate,µ,are all constant.In thatcase,we saw that inflation will be constant and equal toµ.Our model predicts M t/P t=Φ(r+µ,Y).Notice that this impliesM t−M t−1P t =M tP t−M t−1P t−1P t−1P t=Φ(r+µ,Y) 1−11+π =Φ(r+µ,Y)µ1+µ.An increase inπwill make theΦ(r+µ,Y)term smaller,while making theµ/(1+µ)term bigger(you should verify the latter statement by checking thatµ/(1+µ)goes up ifµgoes up).One effect makes revenue smaller while the other makes it bigger.For small values of µ,the latter effect is probably stronger so that revenue should rise asµrises.Eventually, however,we might expect this effect to be reversed.For very large values ofµwe might see Φ(r+µ,Y)→0,whereasµ/(1+µ)→1,implying that revenue might actually get close to 0for very large money growth rates.8.9(a)If you could hold goods between periods(i.e.they were not perishable)and their real value depreciated at the rateδbetween periods,then the“nominal interest rate”to holding them would be given by1+R G=P t+1(1−δ)P t=(1+π)(1−δ).So R G≈π−δ.The interest rate on bonds would still be R=r+π,so it seems unlikely that anyone would actually store the goods as long as R>R G,or r>−δ.The demand for money should still depend on R,and should remain unaffected as long as r>−δ.(b)Since R=r+πe,ifπe rises and R stays the same,r must be falling.If r fell so far that it became less than−δthen people would no longer hold bonds and would switch to storing goods as a way of saving.At that point,the demand for money would depend on the spread between the interest rate on storing goods,π−δ,and the interest rate on money,0. For this reason money demand would probably still fall becauseπe andπwould be rising.8.10(a)Real money demand isΦ(R,Y),so it falls if R rises.(b)People economize on money holdings by going to the bank more often.Therefore, they pay more transactions fees.(c)This implies a negative wealth effect,so C and leisure will fall and L rise.(d)Yes.Leisure also becomes relatively cheap because you don’t have to use money to purchase it.This means C will fall further,and the negative(positive)impact of the rise in R on leisure(labor supply)is mitigated by the substitution effect.8.13The House of Lords was right.By issuing the getting the bank note printers(Waterlow Co.)to deliver them fake notes the swindlers were able to use the fake notes to purchase real goods from the Portuguese economy.In a sense they were able to take some of what would otherwise have been the Portuguese government’s“tax”revenue and use it to purchase goods the Portuguese government could otherwise have acquired.Although printed money is not a claim to anything concrete,it has a value determined by people’s willingness to hold it.As a result,the swindlers were able to acquire goods by doing something only the Portuguese government was allowed to do:i.e.printing money.。
