Consider theexample ofaspeculative bubblein thetext (Section 7.5.2). Now imaginethat while, as before, therearetwo assets, investors no longer have perfect foresight. The privateasset can be purchased at variablereal price qtand pays afixed real dividend

d. Now, however, thereis a probability s that in thefollowing period qt + 1 = 0 (i.e. the bubble will burst), and a probability (1 − s) that it can be sold at qt + 1

> 0. Investors arerisk neutral and equatetherate of return on the government ‘safe’asset r with the expected rate of return on the privateasset.

(a) Write down thearbitragecondition.

(b) Solvefor the‘non-exploding’ value ofcurrent qt