3. Consider a consumer who lives for two periods. Her current-period in- come is y, future-period...

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3. Consider a consumer who lives for two periods. Her current-period in- come is y, future-period income is y and y > y'. She considers her current-period consumption c and future-period consumption d' to be perfect complements. She also likes to perfectly smoothe her consump- tion over time, i.e. c= d. She faces a borrowing rate (r8) that is higher than the rate at which she can lend (r1). There is no limits on her borrowing or lending. (a) Draw a diagram with c on horizontal axis and c' on vertical axis. Draw the above consumer's budget constaint (1 point) and indiffer- ence curve map (1 point). Show her equilibrium (1 point). Is she a borrower on a lender (1 point)? Briefly explain (1 point). (b) The government in her country introduces fully-funded social secu- rity. She is required to contribute t to her social security account with the government. The government promises to pay b in bene- fits in the next period, where b = t (1+ ri). The size of the social security contributions is such that y -t<y+b. In a new diagram, compare her equilibria before and after the introduction of fully- funded social security (5 points). Briefly explain the effect of the introduction of social security on the consumer's welfare (1 point)? (c) Now consider another fully-funded social security scenario. In this scenario, b = t (1+rB). Everything else is the same as in part (b) above. In a new diagram, compare her equilibria before and after the introduction of fully-funded social security (5 points). Briefly explain the effect of the introduction of social security on the con- sumer's welfare (1 point)? 3. Consider a consumer who lives for two periods. Her current-period in- come is y, future-period income is y and y > y'. She considers her current-period consumption c and future-period consumption d' to be perfect complements. She also likes to perfectly smoothe her consump- tion over time, i.e. c= d. She faces a borrowing rate (r8) that is higher than the rate at which she can lend (r1). There is no limits on her borrowing or lending. (a) Draw a diagram with c on horizontal axis and c' on vertical axis. Draw the above consumer's budget constaint (1 point) and indiffer- ence curve map (1 point). Show her equilibrium (1 point). Is she a borrower on a lender (1 point)? Briefly explain (1 point). (b) The government in her country introduces fully-funded social secu- rity. She is required to contribute t to her social security account with the government. The government promises to pay b in bene- fits in the next period, where b = t (1+ ri). The size of the social security contributions is such that y -t<y+b. In a new diagram, compare her equilibria before and after the introduction of fully- funded social security (5 points). Briefly explain the effect of the introduction of social security on the consumer's welfare (1 point)? (c) Now consider another fully-funded social security scenario. In this scenario, b = t (1+rB). Everything else is the same as in part (b) above. In a new diagram, compare her equilibria before and after the introduction of fully-funded social security (5 points). Briefly explain the effect of the introduction of social security on the con- sumer's welfare (1 point)?

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The budget line of the consumer is given as c c 1yr The slope of the budget line is 1r As ... View the full answer