3 ORIGIN OF ASSET PRICE BUBBLES
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investors may change. Note that, on average, behavioral and rational investors agree that the value of the payoff is σ . However, these behavioral agents are like Waermondt and they form their expectations given the signals they receive. To assess the effect of behavioral agents, let us first consider the case in which all investors are rational. In this case, the price of the asset is determined by the arbitrage condition between the two assets. That is, the nonbehavioral price is given by,
pNB =
σ . 1+π
This equation means that agents are indifferent between investing in the storage technology (it has a gross return of 1 + π) and purchasing the risky asset (it has a gross return of σp ). We now introduce behavioral agents in our economy. In this case, we need to find two equilibrium objects: (i) the price of the risky asset and (ii) the agents who purchase this asset. This type of model is characterized by a threshold equilibrium. Let us assume that agents with a signal si above s̄, which will be determined in equilibrium, purchase the risky asset. The rest of agents purchase the riskless asset. We make a parametrical assumption that guarantees that only behavioral investors purchase the risky asset.3 The assumption states that the endowment of behavioral agents is large enough. Given our setup, the two equilibrium objects, the signal of the marginal investor s̄ and the price pB, are given by
s̄ = 1 + π, pB s̄ . pB = eµ 1 − 2σ The first equation characterizes the marginal investor. The investor with signal s̄ is indifferent between investing in the storage technology (the return is 1 + π) and purchasing the risky asset. According to her belief, the payoff of this asset will be s̄, and, thus, the return on the risky asset is 3 In our simple model, the assumption that guarantees that only behavioral investors purchase the risky asset is e > 2σ/µ(1 + π). In words, we assume that behavioral agents have enough wealth.
