Grace consumes leisure (L hours per day) and other goods (Y units per day), with preferences described by U=(L,Y) = L + 2 square root Y. The price of other goods is $1 per unit. The wage rate is w $ per hour.

a). Show how the number of units of leisure Grace chooses depends on the wage rate.

b). How does Grace's daily income depend on the wage rate?

c). Does Grace work more when the wage rate rises?