Keep all settings unchanged, except that, although the

Figure 6.9 Another incomplete network 

The arrows describe the direction of deposit flows, for instance, bank A holds deposits from bank B, and bank B also holds deposits from bank A, etc.

bank is opaque and keeps the entrepreneur's credit report a secret, a late consumer has the option to make an effort to access the credit report in \(t=1\) and then perfectly forecast the project's future return. The late consumer has to incur a cost of \(\sigma\) in her consumption, for the effort in information acquisition.

(a) Suppose that in \(t=1\) the bank offers the same deposit contract \(\left\{d_{L 2}^{G}, d_{L 2}^{B}\right\}\) as in the model to a late consumer. Before depositing in the bank, the late consumer pays \(\sigma\) to access the credit report.
i. Does the late consumer's decision to deposit depend on the future state?
ii. Compute the late consumer's expected utility, with deposit contract \(\left\{d_{L 2}^{G}, d_{L 2}^{B}\right\}\) and information acquisition.
iii. Under what condition will the late consumer deposit in the bank in \(t=1\) without making any effort in information acquisition?
(b) Show that the banking solution breaks down if the condition in question (a) iii. is violated.
(c) Given that the condition in question (a) iii. is violated:
i. Show that the bank can prevent the late consumer's information acquisition and raise deposit from the late consumer, if the entrepreneur's project is divisible, i.e., the entrepreneur only carries out \(\eta\) unit of project, \(0ii. Compute \(\eta\) and the entrepreneur's expected utility.

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