3. (*) Consider two types of firm e e {G, B}. As usual, insiders can observe a firm's type, but investors cannot. The cash-constrained firms have assets in place A and want to invest in a project which requires an investment of I = 60. Capital markets are competitive and interest rates are zero. The table below shows a firm's final value (Z1,Z2,Z3) in the three possible states of the world. Payoffs Z1 Z2 Z3 Assets in place 10 100 100 Growth opportunity 0 0 200 Total payoff 10 100 300 The difference between state 1 and state 2 is in the value of the firm's existing assets. The difference between state 2 and state 3 is in the value of the growth opportunity. The two types G and B differ in the probability of each state of the world (8). Distributions s=1 8=2 8=3 Good-type, PG 0.2 0.4 0.4 Bad-type, PB 0.3 0.4-x 0.3+x In other words, the probability distribution of the three states for the good type is given by pc = {0.2, 0.4, 0.4}, whereas for the bad type it is PB = (0.3, 0.4 - x, 0.3 + x} with a