Answer the following questions: (a) Consider an inter-temporal model with a representative household given by the following utility function: U=t=12(1+1)t1[1(ct)11+lt1+] where >0,0,0 and >0. ct and lt are the consumption and labor in period. t. denotes the minimum level of consumption that a household must consume for surviving in each period. The representative households' endowments in each period are given by 1={l,k} and 2={l,0} respectively, where l>0 and k>0. Derive the inter-temporal budget constraint for the representative consumer. Also, derive the Euler's equation and solve for the consumer's optimum. [20+40=60] (b) The production function of a representative firm in each period is given by Yt=A(1+g)t1(ltl)(ktk)1 where, 00.l>0 and k>0 are the minimum quantity of factors that the representative firm would require to produce a positive quantity of final output. Is the production function neoclassical? What are the profit maximizing factor demands of the firm? [10+30=40] (c) Solve for the inter-temporal competitive equilibrium for the above economy characterized by the representative household and the representative firms with the above preferences, endowments and the production technology. [40] Answer the following questions: (a) Consider an inter-temporal model with a representative household given by the following utility function: U=t=12(1+1)t1[1(ct)11+lt1+] where >0,0,0 and >0. ct and lt are the consumption and labor in period. t. denotes the minimum level of consumption that a household must consume for surviving in each period. The representative households' endowments in each period are given by 1={l,k} and 2={l,0} respectively, where l>0 and k>0. Derive the inter-temporal budget constraint for the representative consumer. Also, derive the Euler's equation and solve for the consumer's optimum. [20+40=60] (b) The production function of a representative firm in each period is given by Yt=A(1+g)t1(ltl)(ktk)1 where, 00.l>0 and k>0 are the minimum quantity of factors that the representative firm would require to produce a positive quantity of final output. Is the production function neoclassical? What are the profit maximizing factor demands of the firm? [10+30=40] (c) Solve for the inter-temporal competitive equilibrium for the above economy characterized by the representative household and the representative firms with the above preferences, endowments and the production technology. [40]