EXPECTATIONS AND MACROECONOMICSThe IS-LM model involves strategic “cheating”.Why? Because most of the components - consumption,investment, etc. - really involve decisions over time. Yet themodel is “static” - it treats current decisions as a function onlyof current variables.That’s OK - you have to simplify. But also necessary to look atthe role of the future in economic decisions - of expectations.Good place to start: interest rates.PV ' V0%V11%i1%V2(1%i1)(1%i2)% ...PV 'V1%i%V(1%i)2% ... 'ViPRESENT VALUES1. What is $1 a year from now worth? I could lend out $1/(1+i), where i is the interest rate, and have $1 a year fromnow. So $1 next year is equivalent to $1/(1+i) now.Or: the present value of $1 one year from now is $1/(1+i)2. Suppose you have a stream of payments coming in (or goingout): V0 now, V1 a year from now, V2 two years from now, etc.And suppose you knew interest rates from now to 1 year fromnow, 1 year to 2 years from now, etc.Then present value of that stream of payments would be3. Special case: permanent payment of V each period, constant i:P 'c1%i%c(1%i)2% ... %1(1%i)nTERM STRUCTURE OF INTEREST RATESA typical bond pays a “coupon” c each year, plus repayment ofprincipal n years from now. Price is expected present value ofthat income stream. Yield is that interest rate at which Yields vary among maturities. If the yield on long-term bonds islower than on short-term, the market is in effect predicting thatinterest rates will fall. If it is higher, de facto prediction thatrates will rise.WHAT DETERMINES INVESTMENT?Think of a project (e.g., building a shopping mall). Is it worthdoing? There will be an initial cost (cost of building the mall),then a future stream of income from the project (rents fromstores, minus expenses). Calculate present value of expectedincome. If it exceeds cost of building, go ahead. If not, don’t doit.So what affects investment:1. Expected earnings from projects. Depends on expected stateof the economy.2. Current and expected future interest rates. (Or long-term ratescorresponding to earnings stream)Think V/i : State of economy affects V, financial conditionsaffect i.PV 'V1%i%V(1%B)(1%i)2% ... 'Vi&BInflation and interest rates:When overall level of prices increases, most things go up intandem - including earnings on investments. Suppose youexpected your shopping mall to yield V real dollars per yearforever. If you now expect inflation at a rate B, then you shouldexpect dollar income of V(1+B) next year, V(1+B)2 the yearafter, and so on.So what’s the present value of an investment that yields a realpayoff V per year?i - B is the real interest rateiYLMISi0i0 +
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