feasible and the optimum consists of solely borrowing from the market. At ...rst the market is constrained by the repayment constraint in the low-repayment-cost state. In this region, the optimal amount of market lending rises with �. As the probability of negative shocks rises, the value of the relationship with private lenders also rises and so does optimal market lending. As � rises further, the constraint becomes irrelevant– this is the part of the red line that is horizontal, and market lending is at the optimal level and independent of �. As � continues to rise, risk-free IFI lending becomes feasible and becomes part of the optimal allocation. As noted above, as IFI lending rises, with higher �, market lending falls in the blended optimum.

To understand the interaction between the market and IFI schedules fully (the red and the green lines) it is useful to note (comparing Figure 5 with Figure 4 or considering Figure 6 below) that when both the market and IFI lenders are present, preferred IFI lending is feasible only for values of � that are higher than those for which, absent market borrowing, IFI lending is feasible. The reason is that the very presence of a market alternative increases the incentives to default on IFI loans. Intuitively, when the VI and the VMB e schedules cross, at � = �, the value of market and IFI lending are the same. Hence, it would be in the country’s interest to default on the IFIs (saving on debt service) and borrow from the market; this makes preferred lending infeasible. For higher values of �, the advantages of IFI lending vis-à-vis market lending are greater and a positive volume of both IFI and market lending may be sustained in equilibrium. But then, at a higher value of � (� = �<sup>c</sup> ), the market is able to also o¤er risk-free loans, and this undermines IFIs’ability to lend risk free and being repaid in equilibrium. Formally, we can prove that Proposition 4 If k 2 [k<sup>b</sup> ; k<sup>a</sup> ] and � 2 (�<sup>a</sup> ; �<sup>c</sup> ), L<sup>�</sup> IB<sup>> 0andthepresenceofIFIsstrictlyimproveswelfare.</sup>

## Proof : In Appendix

As IFI safe lending becomes feasible, it is at ...rst constrained (the optimum is at the frontier of the feasible set) and as � rises, the optimal level of IFI lending increases and market lending falls. At higher values of �, IFI lending becomes unconstrained and the market becomes constrained–this is where the optimum for IFI lending leaves the frontier of the feasible set. In this region, the IFI o¤ers loans at lower interest rates, but which may become onerous to repay in the high-repayment-cost state; in contrast, the market o¤ers loans at higher interest rates but will face default should the high-repayment-cost state materialize. Of course, the higher the probability of requiring emergency lending �, the higher is the appeal of relying on IFI vis-à-vis market lending so that, as � rises, optimal IFI lending also rises, while optimal market lending falls.

In order to better understand the welfare implications of the three di¤erent types of lending, in Figure 6, we plot the value of the di¤erent lending relation (6a), the lending volumes (6b), and the welfare associated with the blended case with that of only the market and only IFI lending–to assess the welfare contribution of IFI lending (6c and 6d).

As discussed, for low values of � (�< e�), market lending is preferred. Things become more interesting in the interval [e�; �<sup>b</sup> ] where IFI lending is optimal but not feasible in the blended case. This is because the very presence of market lenders would induce the country to default on IFIs and thus to be able borrow (solely) from the market. In this region, it would be in the country’s self-interest to be barred from borrowing from private creditors and only borrow from IFIs. The existence of the market reduces welfare in this region and so, if private lending can be barred, in the interval [e�; �<sup>b</sup> ] the country can borrow larger amounts from IFIs and this strictly improves welfare–see Figure 6d. Note that having the possibility of blended lending adds most value (relative to just market) in the intermediate region for �–see Figure 6c.

# 6 Optimal “capital allocation”

Until now, we have assumed that IFIs always have the necessary resources to lend to any particular country as much as they want, provided the amount is compatible with maintaining PCT. However, there may well be quantitative restrictions on the total amounts IFIs can lend. Indeed, greater lending implies larger capital and overhead costs and, while the IMF and MDBs have di¤erent ...nancial models, in the end lending is 14