(a) Solve the rental model of subsection 10.3.1 with two periods when the buyer has two types,…

(a) Solve the rental model of subsection 10.3.1 with two periods when the buyer has two types, and when he has a continuum of types uniformly distributed on [0, 1], say. In particular show that, in the continuum case, there is a “truncation equilibrium” (in which the buyer accepts in period 0 if an only if his valuation exceeds some number)

(b) Show that with a continuum of types and three periods, no truncation equilibrium exists if δ is sufficiently large.

For more on this, see Fernandez-Arias and Kofman 1989.