Question 2 (20 Marks) Consider the recursive equilibrium in Lagos (2010), specifically the case where eq- uities and bonds have different liquidity. We know that of = $" (r;), of = $ (r;) and using my = w(If) = prey. In addition, N = X( ) = V' (n) |+ (It) + :]. and 24 = U' (r,). Also we know, that the government follows the stationary pol- icy Bit1 = B(I,), and that the aggregate state follows a Markov process with P(Ittigri =1} = F(1, I) and that the asset prices satisfy U (x) (x) = B / U' (1) (s') + x] dF(1,I) e' 19|U' (I') BF 1 ) U' ( 2 ) d F ( 1 ', 1 ) Where we = J w (x) dF (r), where [U'(r) dF (r,I) (1) =1- S1to JU(31 8 ] U' (T ) dF (1, 1) Suppose 0 = 1, U (c) = { g, u(q) =4 , and e (g) = q with a > 0 and p > 0. (a) Show that the w (r) can be written as w (It) =1 - (5 Marks) Suppose that Bit = Bry, with 0 5 75 5 (b) Comment on what y =0 and y = 1 imply about the outstanding bond supply (5 Marks) (c) Show that the w (r) can be written as w(1) =1- -1,0 121 1 dF (2141,21) 1 + a (5 Marks) (d) Comment on what this equation implies about the equity premium puzzle (5 Marks) Financial Economics (ECON8037) Page 3 of 5