Problem 3 - Should I go pro?Suppose you are considering becoming a professional athlete. Whilst a pro athlete can expect to make a lot ofmoney when they're young, they may struggle to find gainful employment later in life. If you decide against goingpro, you can expect a much steadier income, though perhaps not quite as lucrative at 21. Which will you choose?Let's set this up formally..Suppose that you live for two periods, t =1,2.If you go pro, in t=1, you will earn Y₁P, which is more than what you would earn in t=1 if you do not gopro, Y₁P. In other words, Y₁P>Y₁np.2.However, in period t=2, as a pro you will earn zero: Y₂P=0. By contrast, Y₂¹P >0.Being a pro athlete makes you a prominent public figure. In period t=1, you have to pay security guards afixed amount S to keep you safe from the mob of fans who stalk your every move on social media.Once your professional career is over, you are quickly forgotten, so you don't have to spend anything onsecurity in t=2.Non-pros have no such problems; they do not pay S in t=1 or t=2.You have well-behaved preferences (you like more consumption, and you have decreasing marginal utilityin consumption in both periods)You can borrow and lend at the rate r against an amount of assets, a.You are selfish! No bequeathments from past generations, and you pass on nothing.First suppose that you do not go pro:1. Write down the dynamic budget constraintDerive the intertemporal budget constraint3. Show graphically the budget constraint and the optimal consumption point in period 1 and 2. Make thediagram large enough for subsequent question parts.Now suppose you do go pro:4. Write down the dynamic budget constraint5. Derive the intertemporal budget constraint6. Using the same graph as in part 3, draw the new budget constraint and the new optimal consumption point.7. Should you go pro? Under what conditions is it better to go pro? Explain.Suppose that the government feels sad for athletes and decides to subsidize retired athletes when they're old. Thiscan't be free! In order to pay athletes the subsidy G in period 2, the government taxes everyone the amount T'inperiod 1. Note that you pay this whether you go pro or not. Furthermore, the government balances its budget suchthat G=T.8. Derive the new intertemporal budget constraints for the pro and non-pro cases in terms of r, C, Y, S, and T.9.Briefly and intuitively, are you more or less likely to go pro under this government policy, and why? If youare an athlete, how much of your tax T will the government eventually 'return' to you?

Budget constraint is a straight slant line, that depicts all the combination of goods that a…

Now suppose you do go pro: 4. Write down the dynamic budget constraint 5. Derive the intertemporal budget constraint 6. Using the same graph as in part 3, draw the new budget constraint and the new optimal consumption point. 7. Should you go pro? Under what conditions is it better to go pro? Explain.

Now suppose you do go pro: 4. Write down the dynamic budget constraint 5. Derive the intertemporal budget constraint 6. Using the same graph as in part 3, draw the new budget constraint and the new optimal consumption point. 7. Should you go pro? Under what conditions is it better to go pro? Explain.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter17: Capital And Time

Section: Chapter Questions

Problem 17.6P

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