Question 2: The CIA model with production In the CIA model that we discussed in class, households are assumed to produce consumption using labour, lt. Assume instead, that there is a profit maximizing firm operating in a competitive market that hires labor at the nominal wage rate of Wt. The firm takes the wage rate as given and produces output according to the production technology shown below: yt=Alt where A>0 is a productivity parameter. All other features of the model are the same. 2.1 Set up the firm's problem and derive the first order condition. 2.2 Set up the household's problem and find the equilibrium level of consumption, leisure and the real interest rate. 2.3 Show how consumption and leisure change with the level of productivity. 2.4 Show that the Friedman rule is optimal for any level of productivity, A. Question 2: The CIA model with production In the CIA model that we discussed in class, households are assumed to produce consumption using labour, lt. Assume instead, that there is a profit maximizing firm operating in a competitive market that hires labor at the nominal wage rate of Wt. The firm takes the wage rate as given and produces output according to the production technology shown below: yt=Alt where A>0 is a productivity parameter. All other features of the model are the same. 2.1 Set up the firm's problem and derive the first order condition. 2.2 Set up the household's problem and find the equilibrium level of consumption, leisure and the real interest rate. 2.3 Show how consumption and leisure change with the level of productivity. 2.4 Show that the Friedman rule is optimal for any level of productivity, A