(Sovereign Default Model) Let if be a risk free rate on the TBills. Let Di be the amount of debt. When the government issues the amount of debt Di and defaults on it, the household consumption with any given 17 E (0,1) in the next period is given by CH1 2 (1 n)Yt+1 0.4Dt (Default) (1) When the government does not default, the household consumption in the next period is given by CH1 : Yi+1 Di (No Default) (2) Finally, the income shock in the next period n+1 is uniformly distributed from 0.5 to 1.5 . That is, the probability density function for n+1 is given by mm) : 1 if 0.5 g yt+1 g 1.5 (3) f(yt+1) = 0 ,otherwise (4) The face value of one unit of this bond is 1, and the fact that the government issues Dt amount of debt means that it issues Dt units of bonds= so that the government needs to pay back Dt to the creditors when it does not default. c) (20 marks) let 2': = 0 and 77 = 0.3. (1) Graph a probability of default as a function of D5 (you can use your pen and pencil for this). The Xaxis is D}; and 19,: 2 0. ii) The unit price of a sovereign bond whose face value is one, is computed in the following: where pd denotes the probability of default for the government. (ii) Graph the bond price as a function of Dt. (iii) The government's revenue for issuing Di amount of debt is 13th (note that Pb is a unit price.) Graph the government's revenue as a function of Di. d) (20 marks): At which Di, the government's revenue is maximized? Let D be the amount of debt which maximizes the governments revenue. Is there any incentive for the government to issue more than D? Argue why this is true or false