Chapter 10 INTERTEMPORAL CHOICE

c2=m2+(m1-c1)+r(m1-c1)= m2+(1+r)(m1-c1) 10.1 The Budget Constraint Intertemporal choices: choices of consumption over time. Saver in the first period consumption Savings: m1- c1 Consumption in the second period c2=m2+(m1-c1)+r(m1-c1)= m2+(1+r)(m1-c1)

10.1 The Budget Constraint Budget constraint Interest rate is zero No borrowing is allowed.

c2=m2-r(c1-m1)-(c1-m1)=m2+(1+r)(m1-c1) 10.1 The Budget Constraint Borrower in the first period Borrower if c1>m1 Interest payments r(c1-m1). Consumption in the second period c2=m2-r(c1-m1)-(c1-m1)=m2+(1+r)(m1-c1)

10.1 The Budget Constraint future value (1+r)c1+ c2=(1+r)m1+ m2 present value c1+ c2/(1+r)= m1+ m2/(1+r)

10.3 Comparative Statics If the consumer chooses a point where c1<m1, she is a lender. If a person is a lender and the interest rate increases, he will remain a lender.

c2= m2 +((1+r)/(1+))(m1-c1) 10.5 Inflation Normalize today’s price to one and let p2 be the price of consumption tomorrow. p2c2=p2m2+(1+r)(m1-c1) c2=m2+((1+r)/p2)(m1-c1) Suppose the inflation rate isπ, we have p2=1+ c2= m2 +((1+r)/(1+))(m1-c1)

10.5 Inflation The real interest rate 1+=(1+r)/(1+) The budget constraint becomes c2=m2+(1+)(m1-c1) The real rate of interest tells you how much extra consumption you can get, not how many extra dollars you can get.

10.5 Inflation 1+=(1+r)/(1+)  =(r-)/(1+) 1+ 1  r- The real rate of interest is just the nominal rate minus the rate of inflation.

10.6 Present Value: A Closer Look A consumption plan is affordable if the present value of consumption equals the present value of income. c1+ c2/(1+r)= m1+ m2/(1+r) The consumer would always prefer a pattern of income with a higher present value to a pattern with a lower present value. A three-period model c1+c2/(1+r)+c3/(1+r)2= m1+m2/(1+r)+m3/(1+r)2

M1+M2/(1+r)>P1+P2/(1+r) 10.8 Use of Present Value Suppose that the income stream (M1, M2) can be purchased by making a stream of payments (P1, P2). Good investment if M1+M2/(1+r)>P1+P2/(1+r) The net cash flow (M1-P1, M2-P2) Net present value of the investment NPV= M1-P1＋(M2-P2)/(1+r)

10.9 Bonds Securities: financial instruments that promise certain patterns of payment schedules. Bonds The coupon x: a fixed number of dollars paid each period; The maturity date T The face value F: the amount paid on the mature date.

10.9 Bonds The present discounted value of a bond: PV=x/(1+r)+x/(1+r)2+…+F/(1+r)T Consols or perpetuities: a bond that makes payments forever. PV=x/(1+r)+x/(1+r)2+…=x/r