2. Consider the life-cycle hypothesis in chapter 17.
- (a) Consider that a consumer who expects to live another T years, has health of W, and expects to earn income Y until she retires R years from now. The consumer wishes to maintain a smooth level of consumption over her life. Assume that interest rate is zero. Derive the consumption function.
- (b) Write the consumption function if consumer expects to live for 50 more years and work for 20 years.
- (c) If a consumer begins adulthood with no wealth, she will accumulate wealth during her working years and then run down her wealth during her retirement years. Assume that consumer has constant income during the period before retirement. Graphically illustrate the consumer’s income, consumption and wealth over her adult life. Make sure to label: the axes and curves.
- (d) Assume that consumer’s income grows over their lifetimes. Graphically illustrate and explain that how does this growth in income influence the lifetime pattern of consumption and wealth accumulation if the consumer can borrow and her wealth can be negative. Make sure to label: the axes and curves.