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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 (TB) that is higher than the rate at which she can lend (TL). There is no limits on her borrowing or lending. (a) Draw a diagram with c on horizontal axis and d'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+r). The size of the social security contributions is such that y-t 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 (TB) that is higher than the rate at which she can lend (TL). There is no limits on her borrowing or lending. (a) Draw a diagram with c on horizontal axis and d'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+r). The size of the social security contributions is such that y-t

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