A very simple model

For pedagogical purposes we consider a simple model with con­stant saving rates, a Leontief technology and a nontraded factor of production which is in fixed supply. Aghion et al.

Thus, consider a small open economy with a single tradable good produced with capital and a country-specific factor. One should typically think of this factor as input services such as (skilled) labor or real estate. We take the output good as the numeraire and denote by p the price of the country-specific factor when expressed in units of the output good. The relative price p can also be interpreted as the real exchange rate. In this basic frame­work we assume that the supply of the country-specific factor is inelastic and equal to Z.

As in the previous chapter, we assume that all agents save a fixed fraction (1 — α) of their total end-of-period wealth and thus consume a fixed fraction α.^[10]

There are two distinct categories of individuals in the economy. First, the lenders who cannot directly invest in production, but can lend out their wealth at the fixed international market-clearing interest rate r. Second, there are the entrepreneurs (or borrowers) who are the people who have the opportunity to invest in production. There is a continuum of lenders and borrowers and their number is normalized to 1 for both categories.

Output y is given by the following production function:

where (1/a) > r, that is, we assume that productivity is larger than the world interest rate. K denotes the current level of capital and z denotes the level of the country-specific input. With perfect capital markets, investment would simply be determined by the international interest rate r.

Credit Market Imperfections: These are modeled as in the previous chapter, namely: an entrepreneur with initial wealth WB can invest at most μWB, whereas they would borrow up to the net present value of their project in the absence of credit constraints. As before the proportionality coefficient, or credit multiplier μ > 0, reflects the level of financial development in the domestic economy, and an entrepreneur with initial wealth WB at the beginning of the period, borrows (μ — 1) Wb = L if her credit constraint is binding.

The Timing of Events: The timing of events within each period t is the following. Investment, borrowing and lending, and the payment of the country-specific factor services p ∙ z by entrepren­eurs to the owners of that factor, take place at the beginning of the period (which we denote by t^-). Everything else occurs at the end of the period (which we denote by t⁺): the returns to investments are realized; borrowers repay their debt, rL, to lenders; and finally, agents make their consumption and savings decisions determin­ing in turn the initial wealth of borrowers at the beginning of the next period (i.e. at (t + 1)^-).