PS 4-24 labor--games

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Feb 20, 2024

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PS 4-24 Labor supply & games TS (she/her/hers) and TK (he/him/his) like to hang out with each other when they get the chance. (I’m using initials instead of names to preserve their privacy.) Unfortunately, neither has a regular job, and their prospects for further advancement in their professions are limited at this point. They want to celebrate (Lunar) New Year’s together and mark the year of the dragon on Saturday February 10. TK, however, has a gig in Las Vegas on Sunday February 11 at 6:30 pm (EST). TS has a gig in Tokyo that ends at 7:30 am (EST) Saturday, and Tokyo is about 12 hours in the air from Las Vegas. TS has a private jet (doesn’t everybody?). Since they don’t have regular jobs, neither can just cancel or postpone these gigs. (Life is tough when you’re a character in an economics problem set.) TS says: “TK, it would be great if you came to Tokyo. Midnight Tokyo is 7am the previous day in Las Vegas. So on Saturday February 10 in Tokyo we would have a full day, starting at midnight to celebrate New Year and dragons. We could stuff ourselves with lucky foods all day—fish and dumplings, spring rolls and sweet rice balls. Then you could come to my gig in the evening. It would be great to have you there. And you’d still have time to get to your gig in Las Vegas. Use my plane if yours is tied up; you can get a good rest on it. I’ll find some way to stream your gig before I go to my next step in Australia. Please, [term of endearment redacted to protect privacy].” TK says: “That would be great. But my gig in Las Vegas is physically and mentally demanding. I wouldn’t really be ready for it if I spent the day before in Tokyo, and that would be bad. Why don’t you come to Las Vegas instead? I’d love to have you with me IRL. You could make it from Tokyo to Las Vegas in time. We could celebrate New Years after my gig and before you go to Australia. Please, [term of endearment redacted to protect privacy].” A payoff matrix can summarize the decisions that face them. TS has two strategies: stay in Tokyo after her gig (call this “TS-Tokyo”); or go to Las Vegas after her gig and watch TK (call this “TS-Las Vegas”). TK also has two strategies, but slightly different: go to Tokyo in time to celebrate the New Year there and watch TS (call this “TK-Tokyo”); or stay in Las Vegas (TK-Las Vegas). TS has the following preferences. Best of all would be for her to stay in Tokyo (TS- Tokyo) and TK to meet her there (TK-Tokyo). Second best for her would be for TK to meet her in Tokyo (TK-Tokyo) and for them to fly back to Las Vegas together (TS- Las Vegas). The problem is that if TK did not do well in his gig she would be blamed for distracting him when he should have been sleeping. Third best would be for him to stay in Las Vegas (TK-Las Vegas) and her to fly there after her gig (TS-Las Vegas). The worst would be for her to stay in Tokyo and him to stay in Las Vegas (TS-Tokyo and TK-Las Vegas) because they would never meet.

TK has the following preferences. Best of all would be for him to stay in Las Vegas and her to fly there after her gig (TS-Las Vegas and TK-Las Vegas). If he went to Tokyo (TK-Tokyo), he would prefer to fly to Las Vegas alone rather than have TS go with him, because of the possible repercussions. So TS-Tokyo and TK-Tokyo is second best and TS-Las Vegas and TK-Tokyo is third best. Worst for him also is TS- Tokyo and TK-Las Vegas where they never meet. I started this payoff matrix. TK chooses row and TS chooses column. I put the payoffs for TS in the appropriate boxes. Then the cats told me that they were hungry so I didn't put the payoffs for TK in. TS-Las Vegas TS-Tokyo TK-Las Vegas 2 0 TK-Tokyo 4 6 1. Complete the payoff matrix. Remember to use greater numbers for more preferred outcomes. 2. Is there a dominant strategy equilibrium? If so, indicate it with a “D” in the payoff matrix you drew. 3. Is there a dominant strategy equilibrium? If so, indicate it with a “D” in the payoff matrix you drew. 4. Is there a Nash equilibrium? If so, indicate it with an “N” in the payoff matrix you drew. Put an “N” in every Nash equilibrium. 5. Put a P in the box for every outcome that is Pareto optimal. Now consider the effect of communication in how the game is played. Suppose both know the payoff matrix, since they know each other well, but aside from the original conversation transcribed above, they have had no communication about what they will actually do. 6. If a means of two-way communication becomes available on which they can talk about what they will do, and this is the only tool they have, would they both be willing to use it? Explain why or why not. 7. Suppose that a means of one-way communication also becomes available. In particular TS can send a message to TK and TK can hear it (or see it), but TK cannot send a message to TS. Suppose TS can decide whether they use the two-way communication device or the one-way communication device. Which will she choose? Explain why.

We talked about the Jamaica controversy in Britain before we studied labor supply. Now that you know labor supply, let’s revisit it. 8. For the supply of labor to field work on sugar plantations, would the substitution effect for an increase in wages for this type of labor lead to more work of this type or less? 9. For the supply of labor to field work on sugar plantations, would the income effect for an increase in wages for this type of labor lead to more work of this type or less? 10.For Afro-Jamaicans working on their own farms before the wage increase, would the substitution effect or the income effect be stronger? Explain why.

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