Suppose that consumers have preferences of the formU(C1) = log(C1) + log(1N1) +[log(C2) + log(1N2)],whereC1andC2are consumption in the first and second period of their lives,N1andN2are theamount of time spent working in the first and second period of their lives, andis the discountfactor.The budget constraints areC1=W1N1B,C2=W2N2+ (1 +r)B,whereW1andW2are the wage rates in the two periods,Bis the amount the consumer saves andris the interest rate.The firm's production function isY1=A1N1,andY2=A2N2,whereY1andY2is output produced in the two periods andA1,A2is the productivity with whichthe firm operates in the two periods.1. Derive the consumer's labor supply curves,N1andN2.2. Solve the firm's profit maximization problem and find the equilibrium wage rates in the twoperiods.3. Use the market clearing conditions (Y1=C1,Y2=C2,B= 0) to find the interest rates as afunction of productivityA1,A2and the discount factor.4. SupposeA2increases. What will happen to output, labor supply, wages and the interest rate?5. SupposeA1increases. What will happen to output, labor supply, wages and the interest