1. Consider a consumer who begins in period 0, with a stock of non-human wealth Ko (ownership of physical capital). The consumer - known as the representative consumer in macroeconomics - is assumed to live forever. In each period t, t= 0, 1, ..., she has 1 unit of time that she supplies in-elasti- cally on the labor market at the wage rate w. The market rate of interest in period t is it. The pre- sent value of the stream of labor income (w;)po, which is the stock of her human wealth, is at + ho = Wo+ Itr, + (1+r, )( 1+r;) ...+ (1+6) (1+;)..(1+r) ;+ ... The sum of her human wealth and non-human wealth is then given by ko + ho- Let c-2 0 be her consumption in period t, t= 0, 1, ... The present value of the stream of consump- tion (Ct) is Co+ Ier, + (dera)(ler ) + + ( 1+r.) (1+5,). (ler,)+... Let u[c] denote her utility in a period, when her consumption in that period is c. Suppose that 6, 0