Question: Consider a modified version of Rochetean and Wright (2013), in this case stocks st (equily claims on firm revenue) can be aulhenitcaled al no cost

Consider a modified version of Rochetean and Wright (2013), in this

Consider a modified version of Rochetean and Wright (2013), in this case stocks st (equily claims on firm revenue) can be aulhenitcaled al no cost in the DM, so lhat they can also be used to facilitate DM trade. Then a household with a portfolio (at,st) obtains yt units of DM output, where yt=ym if (qt+)at+Rtst(y) and (qti)atRtst=(yt) otherwisc. (a) Show that the households problem is given by maxa0,s0{(1qt1qt)qt1a(1Rt)s+(nt)[u(yt)c(yt)]} (5 Marks) (b) Show that the assets have the same rate of return and explain why this must be Whe case (5 Marks) We can show that the number of firms solves {1+(nl)[c(yt)+(1)u(yt)u(yt)c(yt)]}[nt(nt)(1)[u(yl)r(yl)]+f(1)]kf Consider th case where firms have n bargaining powcr in the DM, =1 (c) Show that in steady state the asset price is given by q=f(1)kffkkf (5 Marks) (d) Comment un your results (5 Marks) Consider a modified version of Rochetean and Wright (2013), in this case stocks st (equily claims on firm revenue) can be aulhenitcaled al no cost in the DM, so lhat they can also be used to facilitate DM trade. Then a household with a portfolio (at,st) obtains yt units of DM output, where yt=ym if (qt+)at+Rtst(y) and (qti)atRtst=(yt) otherwisc. (a) Show that the households problem is given by maxa0,s0{(1qt1qt)qt1a(1Rt)s+(nt)[u(yt)c(yt)]} (5 Marks) (b) Show that the assets have the same rate of return and explain why this must be Whe case (5 Marks) We can show that the number of firms solves {1+(nl)[c(yt)+(1)u(yt)u(yt)c(yt)]}[nt(nt)(1)[u(yl)r(yl)]+f(1)]kf Consider th case where firms have n bargaining powcr in the DM, =1 (c) Show that in steady state the asset price is given by q=f(1)kffkkf (5 Marks) (d) Comment un your results

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