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.