ps4_without_solution - Econ 138 Problem Set 4 Professor...

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Econ 138 Problem Set 4 Professor Ulrike Malmendier March 20, 2008 1 More on Asymmetric Information We consider a variation of our standard asymmetric-information model. As before we have two types of fi rms, a fraction μ of ‘H-types’ and a fraction 1 μ of ‘L-types.’ We now assume that fi rms have illiquid assets that are worth either A H (for the H-types) or A L (for the L-types). In addition to having di ff erent assets, the two types also have di ff erent investment projects. The H-types have a project that returns R H with probability p (and returns 0 otherwise). The L-types have a project that returns R L with probability p (and 0 otherwise). Both projects cost I . 1.1 Part 1 (3 points) Suppose the fi rms would like to fi nance investment by issuing equity. We now model issuing equity more realistically, namely as pledging a percentage θ of the company to investors. (In class, we typically assumed a fi xed contingent payment R R m in case of success and 0 in case of failure. As we discussed, this can be interpreted as an equity issuance. In this exercise, we model the equity issuance more directly to illustrate the equivalence.) Let’s fi rst assume that, for a given fi nancing contract that pledges a fraction θ of the fi rm to investors, both types of fi rms would seek fi nancing. How large does θ need to be to convince investors to fi nance a project? (As usual, assume competitive markets for outside
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