Suppose your given the following utility and leisure functions for a typical consumer:
U(Ct, lt) = .4logCt + .6loglt
lt = Ψ(Ct, mt) = (mt).8(Ct)
Where mt = Mt/Pt and all the other variables are as defined in calss. The consumer's budget constraint is
(1 + Rt-1)Bt-1 = [Pt(Ct-Y)+ (Mt - Mt-1)) +(1 + Rt)-1[Pt+1(Ct+1-Y)+ (Mt+1 -Mt)] + ....
(a) What is the difference between money and bonds in this model. Why do people hold money in this model when bonds pay a positive rate of return and money doesn't.
(b) Given the above information, derive the consumer's demand for money in terms of Ct and Rt.
(c) Show whether or not this money demand curve has the usual properties assumed for money demand.
(d) What is the elasticity of money demand with respect to the interest rate? What is the elasticity of money demand with respect to the level of transactions?
(e) In the above model which parameter reflects the sensitivity of "time and energy spent in shopping" to the quantity of money held? What effect would a reduction in the value of this parameter have on the quantity of money held?