**Problem 3 - Should I go pro?**Consider the scenario of becoming a professional athlete. A pro athlete might earn a lot when young but may face challenges finding stable employment later. Opting not to go pro could mean a steadier, albeit less lucrative income at 21. Which path will you choose?Let's formalize the situation:- You live for two periods, $ t = 1, 2 $.- Going pro in $ t = 1 $ means you earn $ Y^p $, more than $ Y $ if you don't go pro, i.e., $ Y^p > Y $.- In $ t = 2 $, as a pro, you earn zero: $ Y^p = 0 $. Non-pros earn $ Y^{np} > 0 $.- Pro athletes become public figures and pay $ S $ for security in $ t = 1 $.- After their career ends, pros are easily forgotten, with no spending on security in $ t = 2 $.- Non-pros face no security expenses at any time.- Preferences favor more consumption with decreasing marginal utility over periods.- You can borrow/lend at rate $ r $ with assets $ a $.- Selfishness means no bequeathments; you pass on nothing.*If you do not go pro:*1. Write the dynamic budget constraint.2. Derive the intertemporal budget constraint.3. Graph the budget constraint and optimal consumption for periods 1 and 2. (Ensure the diagram is large for further questions.)*If you decide to go pro:*4. Write the dynamic budget constraint.5. Derive the intertemporal budget constraint.6. On the same graph as part 3, draw the new budget constraint and optimal consumption point.7. Consider whether to go pro. Under what conditions is it better? Explain.Imagine the government decides to support retired athletes by subsidizing them in old age:- They offer a subsidy $ G $ in period 2, funded by taxing everyone amount $ T $ in period 1 (paid regardless of going pro or not).- The budget is balanced, $ G = T $.8. Derive new intertemporal budget constraints for both pro and non-pro given $ r, C, Y, S, $ and $ T $.9. Consider if this policy influences your

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.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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