Economic help

[Shoppingal]

Bob's preferences for leisure le(in hours) and consumption Y(in dollars) are described by the utility function U=leY.
He sleeps 8 hours a day therefore he has 16 hours/day when he is awake. Wage is $10 an hour. How many hours would he
choose to work per day?

y= 10
le = 8

U = leY
=8(10)
=80

80/16 = 5

he chooses 5 hours a day is this right?

 

[Edmund2011]

let l be the time spent for leisure

Then U = l * 10(16-l) = 160l-10l²
U is to be maximized:

1) Differentiation:
U' = 160-20l

2) find the root:
160-20l=0
l = 160/20 = 8

8 hours spent working
8 hours spent leisure time

 

[Shoppingal]

let l be the time spent for leisure

Then U = l * 10(16-l) = 160l-10l²
U is to be maximized:

1) Differentiation:
U' = 160-20l

2) find the root:
160-20l=0
l = 160/20 = 8

8 hours spent working
8 hours spent leisure time

Could you please explain how you got the 20l?

 

[mmm4444bot]

The power rule for differentiation.

The term a*x^n has derivative n*a*x^(n - 1)

Hence, the term -10*I^2 has derivative 2*(-10)*I^(2 - 1)