Consider an example in the spirit of Leland and Pyle (1977). Unlike in Leland and Pyle (1977), assume that while entrepreneurs are risk-averse (with initial wealth w0 = 100, and utility function of end of period wealth given by U(w1) = E(w1) - 2σw 2 ), all outside investors are risk-neutral.
A) To begin with, assume that there is no information asymmetry in the economy (i.e., all the investors know the true type of firms) at time 0. What fraction of their firm will each type of entrepreneur retain?
B) Now assume that the entrepreneur has private information about her own firm value at time 0, i.e., the entrepreneur knows the type of her own firm, but outside investors only know a prior probability distribution over firm types: outsiders believe that with probability ¼, the entrepreneur’s firm is of type G, and with probability ¾ the entrepreneur’s firm is of type B. What fraction of equity in her own firm will each type of entrepreneur retain in this case (in separating pure strategy equilibrium)?