Suppose that the utility function of a microlender is u = u1 + u2 where u1 and u2 are, respectively, the utility derived from good financial statements and for poverty alleviation. The microlender employs a risk-neutral agent who works eight hours per day. The agent can divide her time between these two activities, namely, between producing good financial statements (i.e., ensuring timely repayments and minimizing costs), and alleviating poverty (i.e., screening the poorer borrowers and instructing them on how to invest wisely). Utility levels u1 and u2 are related to the working hours as follows:

The manager of the MFI can indirectly verify the effort spent on financially oriented activities (e.g., via the repayment rate), but cannot observe whether the agent is contributing to alleviate poverty. The manager of the MFI thus pays the agent accordingly:

A working hour for financially oriented activities costs the agent 7 Rs, and working for alleviating poverty costs 5 Rs. Compute the optimal time allocation for the manager of the MFI, and for the agent. Explain your answer.

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Working hours spent on financial Working hours spent on alleviating poverty activities 1 13 2 18.5 3 23 4 112 6.5 1 13 19 39 2 3 21.5 4 26 10 5 23 5 LO 28 29 30 879 6 25 27 29 678