Consider a Diamond economy without population growth, the production function takes standard Cobb-Douglas form:Y t = K tα L 1 α . t Labor force is constant. Now we extend the standard Diamond model by including the bequest motive. Suppose agents who born in period t also derive utility from the bequest they leave for their decedents. Specifically, utility function for agent born in period t takes form:
Ut =logc1t +βlogc2t+1 +γlogbt+1.
His budget constraint in t and t + 1 are given as follows:
c 1t + s t = w t + b t ,
c2t+1 +bt+1 = st (1+rt+1).
(a) Define kt = K (t) /L (t), show the dynamics of kt+1 as a function of kt. (b) Derive the steady state of k and factor prices, r and w .请问如何消除bt啊,而且bt+1和bt的关系是什么样的呢