(equity multiplier and active monitoring).
(i) Derive the equity multiplier in the variableinvestment model. (Reminder: the investment I ∈ [0, ∞) yields income RI in the case of success and 0 in the case of failure. The borrower's private benefit from misbehaving is equal to BI. Misbehaving reduces the probability of success from pH to pL = pH - ?p. The borrower has cash A and is protected by limited liability. Assume that ρ1 = pHR > 1, ρ0 = pH(R - B/?p) < 1 and 1 > pLR + B. The investors' rate of time preference is equal to 0.) Show that the equity multiplier is equal to 1/(1 - ρ0). (ii) Derive the equity multiplier with active monitoring: the entrepreneur can hire a monitor, who, at private cost cI, reduces the entrepreneur's private benefit from shirking from BI to b(c)I, where b(0) = B, b
- Suppose that the entrepreneur wants to induce level of monitoring c. Write the two incentive constraints to be satisfied by Rm and Rb (where Rb is the borrower's reward in the case of success).
- What is the equity multiplier?
- Show that the entrepreneur chooses c so as to maximize
