Bequest motive in the Diamond model.

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