Consider a consumer who lives for two periods. Her current period income is y and future-period income is y'. Her utility function is U = (1+n)c + c', where n is the population growth rate. She faces a borrowing rate (r_B) that is higher than the rate at which she can lend (r_L). There are no limits on her borrowing or lending.

The government in her country introduces pay-as-you-go social security. She is required to contribute t to her social security account with the government. The government promises to pay b in benefits in the next period, where b = t(1+n). For each of the following three scenarios, draw a separate diagram to show her equilibria before and after the introduction of social security. In all three diagrams, label the budget constraints, the indifference curves, and endowment and equilibrium points. Briefly explain the effect of the introduction of social security on the consumer's welfare in each scenario.

(A) scenario 1: n < r_L < r_B

(B) scenario 2: r_L < n < r_B

(C) scenario 3: r_L < r_B < n