Greta and Godelive are risk-averse entrepreneurs whose utility function is uGo(w) = uGr(w) = √w, where w is the monetary payoff. They have a positive NPV project and need to raise I from risk-neutral outside investors. Godelive has a good idea that generates cash flows CL or Ch with equal probability. Greta has a great idea that generates cash flows CL or CH > Ch with equal probability. Assume risk is diversifiable and the discount rate is zero.
Assume the following values: I = 50, CL = 60, Ch = 80, CH = 140.

 

1) Assume that investors cannot distinguish them, but they believe that the probability that the entrepreneur they face is Greta is 1/3. Consider the possibility of financing with a mix of debt and equity. 

Find the equilibrium of the game? That is, find the outcome in which both Greta and Godelive obtain financing, investors break even, and neither Greta or Godelive has an incentive to deviate.