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Economics 2152A/B
Jennifer Mori

A TWO PERIOD MODEL Chapter 9I DescriptionUp to now all the action in our model economy has taken place during one period It is as if the economy exists for one period in time and then disappearsObviously this is not realistic and we need to remedy the situation When economists deal with changes over time we move from static models to dynamic models This can involve some level of mathematical rigor but we can summarize the gist of a fully dynamic model by simply limiting the number of periods to twoThis is the tack we will take Our two periods will be the current period period 1 and the future period 2 To begin we need to define the agents in our dynamic worldFirst we will have many IDENTICAL consumers who will exist for TWO periods Second we will not consider explicitly the consumption leisure choice made by these consumers but rather their consumption and saving choice Notice we have allowed the consumer to save some of REAL income The reason we can now do this is that we have a second period in which the consumer could consume some of the income produced in the first period Therefore it makes sense to introduce savingOur consumers are price takers in a competitive economy NOTEWe are still dealing with a REAL economy All prices are still denominated in terms of the consumption good So far the only price in our model has been the wage rate We will now add a second price namely the real interest rateOne important concept we must elucidate is date contingent goodsThis is a rather a fancy way of simply saying that goods consumed in the current period are treated as distinct from goods consumed in the second period Simply put current goods and future goods are treated as different goodsThis means that there will be two markets one for current goods and one for future goodsAnother assumption of the model is that consumers prefer to have a smooth consumption pattern over timeThat is to saythat our economy will operate such that goods are demanded in both periods We have set up the description of the dynamic economy now we need to price the goods in the future period II PricingThis is easily done if you recall that in economics generally speaking we are concerned with relative prices For example we can say that diamonds are relatively more expensive that carrots pun intendedHowever it wouldnt matter if the price of a diamond was 100 and the price of a carrot was 1 or if the price of diamond was 1000 and a carrot were 10 What matters is that a diamond is RELATIVELY 100 times more expensive than a carrot Another way of stating this is to set up a ratio of diamonds carrots In this case that ratio would be 100 Thus when we want to engage in exchange we need 100 times more consumption units to trade for 1 diamondNow map this idea onto our problem at hand In order to price future goods all we need to do is relate their value to current goods Number of current goods number of future goodsSuppose our consumer was willing to give up 5 units of consumption todayie save 5 unitsfor 10 units of consumption in the future Now our price ratio would be 5 units of current consumption10 units of future consumption This equalsor 5 Thus we would say that the the price of future goods is 5 current goods Now lets make this a little more realistic Notice the model adds more realism as we continue to construct itWe cant really trade something between time periods We cannot transport goods produced today into the future However we can promise to give someone goods we produce in the future in exchange for goods today This promise can be thought of as a bondAn old expression is My word is my bond This means that your promise your word is a good and binding contractA bond is therefore just a debt instrument that is a promise to pay in the futureNow this means that the market for future consumption will be in fact a credit market In this credit market agents will exchange promises or bondsTherefore in the current period if someone wants to exchange present goods for future goods they will enter the credit market and buy bonds Alternatively if someone wants toexchange future consumption for consumption in the current period they will enter the credit market and sell bondsWe have just modeled a bond marketdemanders and suppliersbuyers and sellers of bondsAs in all markets this exchange will take place at a price and this price is called the real interest rate rThus the real interest rate will be the rate at which current goods trade for future goodsIf you dont want to consume all your production in the present period you can now save some of it and lend it in the credit market at a rate of interest
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