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S. BASCO
in (steady-state) equilibrium (Eq. 3.8). If we apply this condition to a financially developed economy, Eq. (3.8) becomes
B = AU − DU = aU (1) − d U (δ, 1) > 0.
(4.9)
Is this condition satisfied if the country is financially developed? The answer depends on the depreciation rate of houses. If the depreciation rate is small, the supply of assets will be high and condition (4.9) will not be satisfied. In contrast, if the depreciation rate is very large, the supply of assets will be small and condition (4.9) will be satisfied. As we have seen in the previous chapter, rational bubbles may emerge in equilibrium when the supply of assets is small. In other words, if we have a high δ, the model is like the standard Samuelson model we discussed above. From now on, we assume that the depreciation rate is small. To be precise, we assume that δ < δ ∗, where δ ∗ is implicitly defined by aU (1) = d U (δ ∗ , 1). As we have discussed, this assumption implies that there is no shortage of assets in the financially developed country. In other words, rational bubbles cannot emerge in the financially developed country if it remains in autarky. We are now ready to analyze the effect of letting the financially developed country trade with the financially underdeveloped country. In the absence of rational bubbles, the free trade equilibrium can be described by the following capital market clearing condition.
AU + AC = DU + DC .
(4.10)
The left-hand side of Eq. (4.10) is the world demand of assets in the economy (i.e., the sum of the demand of assets in country U, AU , and the demand of assets in country C, AC). Analogously, the right-hand side of the equation is the world supply of assets. There exists a unique equilibrium interest rate that clears the world capital market.4 In other words, given this interest rate, the world supply of assets equals the world demand of assets. Figure 4.2 represents the capital market of the financially underdeveloped economy (left-hand side) and the capital market of the financially 4 It can be shown that the fundamental (or non-bubble) equilibrium is unique under mild conditions. See Basco (2014) for the exact condition. Basically, it can be shown that the supply of assets (D) monotonically decreases with the interest rate. Similarly, the demand of assets (A) increases with the interest rate provided that the index of the quality of financial institutions of country C, Ɵ, is low enough.
