In this paper, x and у will denote, respectively, the typical agent’s consumption in period 1 if she turns out to be impatient, and in period 2 if she turns out to be patient. Then the expected utility of the representative agent can be represented by:
We choose a specific functional form to obtain closed-form solutions and facilitate the analysis that follows.
In this setup, as in the classic Diamond-Dybvig (1983) formulation, domestic residents face uncertainty about the timing of consumption and also a pattern of asset returns such that they would prefer to invest in the world market if they knew they were impatient, and in the illiquid technology if they knew they were patient. A new feature of the model is the openness of the economy. This introduces a number of new features into the model, as will become apparent below.
A commercial bank
Clearly, if each domestic agent acted in isolation from the others, each one would bear idiosyncratic risk; in particular, costly liquidation of the long term technology would often occur with positive probability. The absence of uncertainty in the aggregate implies that improvements may be attainable if, as we shall assume from now on, domestic agents act collectively; their coalition will be called a “commercial bank” (or simply “bank” when no confusion may arise) for reasons that will be clear shortly.
The objective of the bank is to pool the resources of the economy in order to maximize the welfare of its representative member. This requires assigning a consumption stream to each agent contingent on the realization of her type. In choosing such a contingent allocation, the bank is restricted not only by resource constraints but also by fact that type realizations are private information. This implies that the bank must find some way of eliciting such information.
While examining all of the bank’s options would be exceedingly complex, the Revelation Principle6 implies that attention can be restricted to feasible type contingent allocations that give no agent an incentive to misrepresent her type. As a consequence, the bank will choose an allocation to solve a relatively simple problem. Let d and b denote net foreign borrowing in periods 0 and 1, respectively, and let к be the amount invested in the domestic (illiquid) asset. The bank maximizes 1 subject to:
where I denotes liquidation of the domestic asset in period 1. The above problem will be referred to as the basic social planning problem, and its solution, the social optimum, will be denoted by tildes. fast cash payday loans