Consider the previous exercise and suppose that the introduction of social security induces the individuals to retire in period 2. So they receive no labor income in period 2.
a. What is the new optimal consumption in each period? How much do the consumers save? How does it compare with previous exercise? Explain.
b. Now building on this example, should the actual social security system lead to early retirement? Why or why not? What is the evidence on the impact of social security on the retirement decision in the United States and elsewhere?