14 Overlapping generations with linear preferences Suppose that we have an overlapping generations model in which agents have linear preferences over consumption U = Cut + Bent+1 The production function is Cobb-Douglas. a) Define the consumer's problem, the firm's problem, and equilibrium. b) Find the savings rate of the young worker as a function of /r+/. Is savings increasing or decreasing in the interest rate? c) Find a difference equation expressing katy as a function of k. d) Find the steady state capital stock