Consider a small open economy populated by a large number of ex ante identical agents. There are three periods indexed by t = 0,1, 2. There is only one good, which is freely traded in the world market and can be consumed and invested. The price of consumption in the world market is fixed and normalized at one unit of foreign currency (a “dollar”). Hence, we will speak interchangeably of dollars or units of consumption. Domestic residents are born with an endowment of e > 0 units of this good (worth e dollars) each website.
Each agent is also endowed with access to a constant returns long term technology whose yield per dollar invested at t — 0 is r < 1 dollars in period 1, and R > 1 dollars in period 2. That is to say, the long term technology is illiquid: it is very productive if the investment is held for two periods, but early liquidation causes a net loss of (1 — r) > 0 per dollar invested. Only domestic residents have access to this technology.
In addition, there is a world capital market where one dollar invested at t = 0 yields one dollar in either period 1 or period 2. Domestic agents can invest as much as they want in this market, but can borrow a maximum of / > 0 dollars. While we will treat the credit ceiling as exogenous, it could be justified by recourse to the many theories of international borrowing under sovereign risk. It can also be thought of as the result of domestic restrictions (a regulated capital account) that prevent domestic residents from borrowing more than / dollars.
Clearly, domestic consumption will be increasing in e. Also, domestic consumption will be rising in /, because the domestic technology has a higher return than the world rate of interest. For instance, if in period 0 an agent borrowed up to the full credit ceiling e, invested all of the loan proceeds in the domestic technology, and held the investment for two periods, her total resources available for consumption in period 2 would be eR + f (R — 1) > 0 dollars.
Domestic agents face a non trivial decision, however, because they may be forced to consume early. We will assume, as in Diamond and Dybvig (1983), that at t = 1 each domestic agent discovers her “type”. With probability Л she is “impatient” and derives utility only from period 1 consumption. With probability (1 —A) she turns out to be “patient” and derives utility only from period 2 consumption. Type realizations are i.i.d across agents, and there is no aggregate uncertainty We shall also follow Diamond and Dybvig (1983) in assuming that the realization of each agent’s type is private information to that agent.