4. (25%) Consider a simple two-period model where the world lasts only for two periods. An agent has one unit of labor and provides the labor to the market inelastically. The agent's budget constraints in the two periods are:

$$c1 + b1 = w_1$$

$$c2 = b1(1 + r1) + w2$$

where b1 is the asset position of the agent in period 1, w1 and w2 are the real wage rate in periods 1 and 2, and r1 is the real interest rate from period 1 to period 2. The production technology in this economy is

$$Y = AL$$

for both periods, where L is total number of workers or agents in the economy. All markets are competitive. Answer the following questions.