Suppose you are an amateur athlete and your uncle owns the cereal company “Wheaties.” Your uncle offers you a job working for his company at a wage of w per hour. After looking around for other jobs, you find that the most you could make elsewhere is w′, where w′ < w. You have a weekly leisure endowment of L and can allocate any amount of that to work. Given the higher wage at Wheaties, you accept your uncle’s job offer.
A: Then you win a gold medal in the Olympics. “Greeties”, the makers of grits, ask you for an endorsement. As part of the deal, they will pay you some fixed weekly amount to appear on their boxes of grits. Unfortunately, your uncle (who hates his competitor “Greeties” with the white hot intensity of a thousand suns) will fire you if you accept the deal offered by “Greeties”. Therefore, if you accept the deal, your wage falls to w′.
(a) On a graph with Consumption on the vertical and Leisure on the horizontal axis, graph your budget constraint before the “Greeties” offer.
(b) On the same graph, illustrate your budget if you worked for someone other than your uncle prior to your success in the Olympics.
(c) Illustrate the minimum amount that “Greeties” would have to pay you (weekly) for your endorsement in order for you to accept the deal. Call this amount E.
(d) How does this amount E compare to the amount necessary to get you to be able to consume bundle A under a Greeties endorsement deal?
(e) Now suppose that you accepted the endorsement deal from “Greeties” but, unfortunately, the check for the endorsement bounces because “Greeties” goes bankrupt. Therefore the deal is off, but your angry uncle has already fired you. Deep down inside your uncle still cares about you and will give you back your old job if you come back and ask him for it. The problem is that you have to get past his greedy secretary who has full control over who gets to see your uncle. When you get to the “Wheaties” office, she informs you that you have to commit to pay her a weekly bribe if you want access to your uncle. On a new graph, illustrate the largest possible (weekly) payment you would be willing to make. Call this F.
(f) If your uncle’s secretary just asks you for a weekly bribe that gets you to the bundle C that you would consume in the absence of returning to Wheaties, would you pay her such a bribe?
(g) Suppose your tastes are such that the wealth effect from a wage change is exactly offset by the substitution effect — i.e. no matter what the wage, you will always work the same amount (in the absence of receiving endorsement checks or paying bribes). In this case, can you tell whether the amount E (i.e. the minimum endorsement check) is greater than or equal to the amount F (i.e. the maximum bribe)?
B: Suppose that your tastes over weekly consumption c and weekly leisure ℓ can be represented by the utility function u(c, ℓ) = c0.5ℓ0.5 and your weekly leisure endowment is L = 60.
(a) If you accept the initial job with Wheaties, how much will you work?
(b) Suppose you accept a deal from Greeties that pays you a weekly amount E. How much will you work then? Can you tell whether this is more or less than you would work at Wheaties?
(c) Suppose that the wage w at Wheaties is $50 per hour and the wage w′ at Greeties (or any other potential employer other than Wheaties) is $25 per hour. What is the lowest possible value for E — the weekly endorsement money from Greeties — that might get you to accept the endorsement deal?
(d) How much will you work if you accept this endorsement deal E?
(f) How much would you work assuming that the secretary has successfully extracted the maximum amount you are willing to pay to get your Wheaties job back?
(g) Re-draw your graphs from part A but now label all the points and intercepts in accordance with your calculations. Does your prediction from A (g) about the size of the maximum bribe relative to the size of the minimum endorsement hold true?