# AdverseSelectionProblem - Economics 423 Josef Perktold...

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Economics 423 Josef Perktold Project Financing, Adverse Selection and Self-Selection Entrepreneurs need to °nance a project of a °xed size K that can either give a high positive return of R; so that next period the wealth is (1 + R ) K; or the project turns out to be unpro°table and the °rm looses even the capital that was invested in the project, the wealth of the project is zero. The high return occurs with probability ° (the loss occurs with probability 1 ° ° ). Project di/er in their success probability, a fraction ± 1 = 1 = 2 has the low success probability ° 1 = 0 : 4 , and a fraction ± 2 = 1 = 2 has the highest success probability ° 3 = 0 : 8 : Entrepreneurs or °rms know the success probability of their projects. If an °rm does not invest in the project, then the pro°t is zero. Entrepreneurs can invest their own money. The cost of raising funds is given by the rate c B ; the total cost of raising an amount of K Dollars is (1 + c B ) K: Entrepreneurs can also borrow from a competitive banking industry. The cost of raising funds by banks is given by the rate c L ; the total cost of raising an amount of K Dollars is (1 + c L ) K: The banking industry has many °rms competing for customers. ° 1 = 0 : 4 ; ° 2 = 0 : 8 R = 3 ; c B = 0 : 4 ; c L = 0 : 2 ; K = 1 ± 1 = ± 2 = 1 = 2 ( Remark: This numbers have been chosen so that the calculations are easy. Do not be surprised if the interest rates are large.) a) Suppose entrepreneurs do not have access to borrowing and have to raise their capital inter- nally. Which entrepreneurs will invest and what is the pro°t of each entrepreneur.

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