1 Consider an economy populated by a representative household that lives forever. Time is discrete. Household's preferences are given by Z ilulctal htll- (1) 20 with 6 (0,1). The budget constraint is Ct 'l' kt+1 S will: + (1 'l' 7"; (\"km (2) where all variables have the usual interpretation and (5 6 (0,1). In each period 15, static firms produce final goods with a neoclassical production function of labour and capital Akf, hf) where A > 0, and kg and hf are the demands for labour and capital inputs. Firms sell final goods and hire labour and capital from the household in perfectly competitive markets. Feasibility requires that ct + km 3 Akt, h.) + (1 5m. (3) (a) State the properties of the utility function 'u. that guarantee that the problem of the household is concave and the solution is interior. (b) State the planner's problem and find the first order conditions. (c) Find the first order conditions for the consumer and for the firm and define the market clearing conditions for a competitive equilibrium. (d) Show whether the equilibrium is efficient