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PS3_contract theory

# PS3_contract theory - oﬀer to the investor at...

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PROBLEM SET 3: SIGNALING 1. Collateral as a signaling device Consider a risk-neutral entrepreneur who needs \$ I to finance a project. If fi- nanced, the project will yield profit R with probability θ and 0 with probability 1 - θ . Everyone knows there are two types of entrepreneurs in the market: High type entrepreneurs have a probability of success θ H > 0, while low types have a probability of success θ H > θ L > 0. Also, everyone knows that there is a fraction β > 0 of entrepreneurs with type L. We assume that θ L R - I > 0. The entrepreneur has no cash, and thus, needs to find funding from a risk-neutral outside investor. We assume that the entrepreneur gets to make a take-or-leave offer to the outside investor for the financial contract. (1) If the entrepreneur’s probability of success is observable, what financial contract will each type of entrepreneur offer to the investor? (2) Assume from now on that the entrepreneur’s type is private information to the entrepreneur. What is the contract that each entrepreneur’s type will
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Unformatted text preview: oﬀer to the investor at equilibrium. (3) Assume now that the ﬁrm also has the possibility of pledging some assets as collateral for the loan: if the ﬁrm makes 0 proﬁt, an asset of value K to the entrepreneur is transfered to the creditor whose valuation for the asset is x.K , with x < 1. The size of the collateral pledged to the investor is a choice variable for the entrepreneur. (a) Intuitively, why would collateral pledging be an eﬃcient signaling de-vice in this context? (b) Find the separating equilibrium that provides the H type entrepreneur with the highest utility. (c) Find the pooling equilibrium that provides the H type entrepreneur with the highest utility. (d) When is it the case that the high type entrepreneur prefers the pooling equilibrium of question 3.c to the separating equilibrium of question 3.b? How does it depend on β and x ? Discuss. 1...
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