Chapter 3 The Behavior of Households with Markets for Commodities and Credit In this chapter we move from the world in which Robinson Crusoe is alone on his island to a world of many identical households that interact. To begin, we consider one particular representative household. When we add together the behaviors of many households, we get a macroeconomy. | Chapter 3 The Behavior of Households with Markets for Commodities and Credit In this chapter we move from the world in which Robinson Crusoe is alone on his island to a world of many identical households that interact. To begin we consider one particular representative household. When we add together the behaviors of many households we get a macroeconomy. Whereas in Chapter 2 we looked at Crusoe s choices between consumption and leisure at one point in time now we consider households choices of consumption over multiple periods abstracting from the labor decisions of households. Section introduces the basic setup of the chapter. In Section we work out a model in which households live for only two periods. Households live indefinitely in the model presented in Section . Both these models follow Barro fairly closely but of course in greater mathematical detail. The primary difference is that Barro has households carry around money while we do not. The Genaral Sutup The representative household cares about consumption q in each period. This is formalized by some utility function 7 c c2 c3 . . Economists almost always simplify intertemporal problems by assuming that preferences are additively separable. Such preferences look like t7 ci c2 c3 . . u ci u c2 2u c3 . The u - function is called the period utility. It satisfies standard properties of utility functions. The variable is called 22 The Behavior of Households with Markets for Commodities and Credit the discount factor. It is just a number say . The fact that it is less than 1 means that the household cares a little more about current consumption than it cares about future consumption. The household gets exogenous income in each period. This income is in terms of consumption goods. We say that it is exogenous because it is independent of anything that the household does. Think of this income as some bequest from God or goods that fall from the sky. At time t the household can buy or sell .
