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Problem. 3-Consumption \& Asset Pricing Consider a representative individual who maximizes utility, U, given by CRRA U(Ct,PtMt,Nt)=Et{t=0t[1Ct1+1a(PtMt)11+bNt1+]} where, Ct is the total consumption, PtMt is real currency and Nt hours worked. At ,,>0 representing the relative risk aversion coefficient, elasticity of money demand and elasticity of labour supply, respectively. Budget constraint is: PtCt+Mt+(1+it)1Bt=WtNt+Bt1+Mt1+Tt+t As usual, Bt the investment made in the risk-free asset in period t for redemption in t+1;Mt are nominal amounts of currency acquired in t;Mt1 are nominal amounts of currency acquired in t1 that are taken into t;Bt1 is the risk-free stock of the asset carried between t1 and t;Tt represents lump-sum government transfers; t is the profit distributed by the firm; Wt denotes the nominal wage and it corresponds to the nominal risk-free interest rate. a) Derive a money demand function for this economy. Explain the equation obtained. [Hint: Use Bellman equation.] b) Derive Euler equation for consumption. Solve for the representative individual optimal consumption: Ct. Problem. 3-Consumption \& Asset Pricing Consider a representative individual who maximizes utility, U, given by CRRA U(Ct,PtMt,Nt)=Et{t=0t[1Ct1+1a(PtMt)11+bNt1+]} where, Ct is the total consumption, PtMt is real currency and Nt hours worked. At ,,>0 representing the relative risk aversion coefficient, elasticity of money demand and elasticity of labour supply, respectively. Budget constraint is: PtCt+Mt+(1+it)1Bt=WtNt+Bt1+Mt1+Tt+t As usual, Bt the investment made in the risk-free asset in period t for redemption in t+1;Mt are nominal amounts of currency acquired in t;Mt1 are nominal amounts of currency acquired in t1 that are taken into t;Bt1 is the risk-free stock of the asset carried between t1 and t;Tt represents lump-sum government transfers; t is the profit distributed by the firm; Wt denotes the nominal wage and it corresponds to the nominal risk-free interest rate. a) Derive a money demand function for this economy. Explain the equation obtained. [Hint: Use Bellman equation.] b) Derive Euler equation for consumption. Solve for the representative individual optimal consumption: Ct