Q2. (35 points) In the previous question Q1, the financial institutions were able to provide the financial intermediation services without any cost. In question Q2, assume the same economy except that the financial intermediation services are now costly, and the financial intstitutions charge the cost by setting the lending interest rate (11) higher than the deposit interest rate (ra). Let x = 1( r ra) > 0 be the spread between the lending and deposit interest rates. The spread x captures the inefficiency of the financial intermediation technology of this economy. Assume that x is exogenously given. 1+11 1+ra (a) (5 points) Formulate type-A households' optimization problem using the intertemporal bud- get constraint and solve their optimal consumption CA and c and optimal saving S^. Similarly, formulate type-B households' optimization problem using the intertemporal budget constraint and solve their optimal consumption c and c and optimal borrowing bb. (If you are obtaining type-A and type-B households' optimal choices by revising your answers in parts (c) and (d) of Q1 rather than applying the Lagrangian method repeatedly, explain precisely the reason why you can do so.) (b) (5 points) Derive the aggregate bond supply (Sbond) and the aggregate bond demand (Dbond) in this economy. Then, determine the equilibrium interest rates r and r* using the bond market clearing condition. From now on, you will compare the economy under x = 0 and the economy under x > 0. To distinguish these two economies, denote the interest rate and consumption bundles in the former economy (x 0) as rxz, xz, xz, c) xz, and c) xz, and denote the interest rates and consumption bundles in the latter economy (x > 0) as r* xp, r xp, c xp, C^ xp, cxp, and c) xp. (The subscript xz is an abbreviation for 'x is zero', and xp is an abbreviation for 'x is positive.') = (c) (5 points) Prove that r* r*,xp 0 by using the revealed preference argument.