Consider a stock that pays dividends of Dt in period t and whose price in period t is Pt. Assume that consumers are risk-neutral and have a discount rate of r; thus they maximize E [

∞

t =0 Ct/(1 + r)

t ].

(a) Show that equilibrium requires Pt = Et[(Dt +1 + Pt +1)/(1 + r)] (assume that if the stock is sold, this happens after that period’s dividends have been paid).

(b) Assume that lims→∞ Et[Pt +s/(1 + r)

s ] = 0 (this is a no-bubbles condition; see the next problem). Iterate the expression in part

(a) forward to derive an expression for Pt in terms of expectations of future dividends.