We illustrate now the impact of changing the “generosity” of a deposit insurance scheme. For simplicity of exposition, we follow the assumptions of Section 2, where only idiosyncratic risk is present. Suppose that banks anticipate a partial bailout. Specifically, suppose that banks expect that, if their net income is negative, a fraction of the non-performing loans will be repaid by the public sector. In these circumstances banks’ expected profits (6) are modified to
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Deposit insurance reduces the marginal cost of risk from the bank’s point of view [the LHS of (7a1)], encouraging thereby risk undertaking. While deposit insurance does not impact the expected output of a given project (nor does it affect the socially optimal risk), it “socializes” part of the risk. Hence, banks would increase the project’s risk tolerated. The net effect is increasing the excessive risk distortion. This point is exemplified in Figure 5, panel II, tracing the excessive risk as a function of the bank’s cost of funds.

The curve is drawn for the parameter values used in Figure 4, panel I. The efficient risk is traced by curve OO. The top curve corresponds to a competitive equilibrium, where ¥ = 0.05, and the middle curve corresponds to the competitive equilibrium in the absence of deposit insurance (¥ = 0). As suggested by (7a’), deposit insurance increases the risk tolerated by banks, magnifying the excessive risk distortion. Consequently, as in to the previous discussion, deposit insurance increases the range where financial liberalization would be welfare reducing.