Question 3 (20 Marks) Consider a modified version of Rocheteau and Wright (2013), in this case stocks at (equity claims on firm revenue) can be autheniteated at no cost in the DM, so that they can also be used to facilitate DM trade. Then a household with a portfolio (at, at) obtains y units of DM output, where yo = y' if (q + x)o, + Rig, 2 w (y' ) and (ne + k) at + Rest = w (y) otherwise. (a) Show that the households problem is given by MAX 030,320 41-1 410-(81 - R) 8 + (m)Ou(y) - e()] (5 Marks) (b) Show that the assets have the same rate of return and explain why this must be the case (5 Marks) We can show that the number of firms solves "' (3) -' (y) B 1 + (14) Be ( M1 ) + ( 1 - # ) w (tt ) -(1 - #) lu(ye) - e(all + f(1) = N The Consider the case where firms have no bargaining power in the DM, # = 1 (c) Show that in steady state the asset price is given by Kkf 4 = f (1) - k (5 Marks) (d) Comment on your results