Answer to Question #249043 in Microeconomics for SHREYA

Question

Suppose Lionel Messi was making the choice of how many hours to practice. Messi knows that there is a positive relationship between the number of hours he practices and the number of goals he scores in a season at Barcelona. Numbers in the table below denote combinations of free time and goals for Lionel Messi, given his preferences of goals vs free time is known and his ability is unchanged within the season. There are no lucky goals, his productivity only depends on the number of hours he practices.

X Y Z

Free Time 12 21 18

Goals 95 41 68

MRT 3 9 6

MRS 25 4 6 

At point X, will Messi want to increase his consumption of free time or reduce it? Why? 

At point Y, will Messi want to increase his consumption of free time or reduce it? Why? 

At point Z, will Messi want to increase his consumption of free time or reduce it?

Why? 

Answer 1

1. At point X, Messi will want to increase his consumption of free time because at this point, he has scored the maximum number of goals (95) and the marginal rate of substitution of goals for free time is high (25). The probability of scoring more goals is quite low (at 3), hence, the probability of having more free time is high.
2. At point Y, Messi will want to reduce his consumption of free time because at this point, he has scored the lowest number of goals(41). MRS of goals for free time is low ( at 4) because he has to practise more in order to score more goals. MRT is highest (at 9), Messi will have to forego Free time in order to practise more so as to attain more goals.
3. At point Z, MRT=MRS. At this point, Messi has maximized his utility and he will either want to increase his consumption of free time or reduce it according to his own will because he is at a point of satisfaction.