Consider our analysis of the utility-maximizing retirement age for Linda
Consider our analysis of the utility-maximizing retirement age for Linda, where she makes this choice based on her annual wage w, and her preferences for consumption c and leisure ℓ. Assume that both c and ℓ are normal goods for Linda, and suppose she has 20 years of remaining potential work-time available.
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(b) Illustrate her utility-maximum point X if she decides to choose ℓ such that ℓ = 20, and she now realizes that she wishes she had retired 3 years earlier (i.e., when she had 23 years of time left). How, at point X, does her marginal utility from ℓ compare with her marginal utility from c? What does this represent, in practical terms?
(c) Illustrate her utility-maximum point X if she decides to choose ℓ such that ℓ = 0. Consider all possible cases. How, at point X, does her marginal utility from ℓ compare with her marginal utility from c? Consider all possible cases. What does each of these cases represent, in practical terms?
(d) Returning to the context of part (a), suppose now that she discovers that her annual wage is lower than she originally expected—it has fallen from w1 to w2 (where w1 > w2). At this lower wage of w2, will she decide to retire earlier or later, compared to what she planned to choose when the wage is w1? Explain how her decision reflects the impacts, logically, of a lower wage.
(e) Returning now to the context where the wage is w1, suppose she now learns that she is eligible for a pension equal to $b each year she is in retirement (i.e., not working). (Assume that w1 > b.) Now that she is aware that she can get this pension benefit, will she retire earlier or later as compared to what she would do if there was no pension benefit (i.e., the choice she makes in part (a))? Why, logically, does she make this decision?
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