Suppose a consumer who has to decideif she wants to go to pro or not. If she does NOT go, she will get a low income in both periods, Y1, Y2. If she goes pro, she will get a higher wage in the rst period Y: 3 I]. In the second period, she 1will have NO income (Y; = U] and, in addition, she will have to pay and extra amount 5' to sustain her fancy lifestyle in the second period. She has increasing and concave preferences over consumption in the two periods (01 and 6'2] Consider first that she does not go pro 1. Write down the dynamic budget constraints 2. Derive the intertemporal budget constraint 3. Show graphically the budget constraint and the optimal consumption point in period 1 and 2. 1 If she decides to go pro, 4. Write down the dynamic budget constraints 5. Derive the intertemporal budget constraint 6. In your previous graph, draw the new budget constraint and the new optimal consumption point. I". [s it good for her to go pro? Under what conditions will shebe better off by going pro rather than not going pro? Explain. 8. [f the go tsubsidizes the retired athletes in the second period, and the consumer has to pay this social security in the first period (discounted by the interest rate), it is more likely that she optimally chooses to go pro?. Discuss the validity of this statement