Question

Problem 1. Consider the problem of an agent at date t, who marimizes the utility function に0 subject to a sequence of budget constraint, where B is the discount factor, c+k is consumption in period t+ k and 1/η is the intertemporal elasticity of substitution Let P+k be the price level prevailing at date t+k, i.e. Pt+k Dollar buy 1 unit of the consumption good in period t +k. Among the various assets that the agent can trade at date t are k-period discount bonds, who promise to pay 1 Dollar in period t +k and nothing else. Denote the date-t Dollar price of such a bond by Qtt+k. Assume that the agent can both buy and sell at that price. Let stt+k be the quantity of these k-period discount bonds, which the agent buys in period Some more notation. Let δ--log(β) be the discount rate of the agent. where here and everywhere else, log denotes the natural logarithm (not the log- arithm to the basis of 10). Let 9+log(u) - log(k-1) klog(c+k)-log(c+k-1) denote the grouth rate of consumption from t +k-1 to tk. Let be the corresponding inflation rate. Define ytt+k as t,t+k We assume throughout that Qtt+k is reasonably close to 1 and that gt+k and Tt+k are reasonably close to zero

Answer 1

• A nominal interest rate is the interest rate that does not take inflation into account.It is the interest rate that is quoted on bonds and loans.The disadvantage of the nominal interest rate is that it does not adjust for the inflation rate.
• A real interest rate is the interest rate that does take inflation into account.As opposed to the nominal interest rate ,the real interest rate adjust for the inflation and gives the real rate of loan or a bond.To calculate the real interest rate you first need the real interest rate.