A park has a capacity to hold 60,000 people on any particular day.
Using third degree price discrimination - demand for 2 groups (boys & girls)
Q /6000 + P = 8 Q / 6000 + P = 6
b b g g
The hint provided is: Marginal Revenue in the two markets must be equal
How do I figure out what to charge for admission to the boys and girls respectively?
Let's first set each demand as Price as a function of Quantity:
For boys (let's call Qb and Pb to their quantity and price)
Qb/6000 + Pb = 8
Pb = 8 - Qb/6000
Qg/6000 + Pg = 6
Pg = 6 - Qg/6000
Total profits from the sales of tickets are thus:
Pb*Qb + Pg*Qg = (8 - Qb/6000)*Qb + (6 - Qg/6000)*Qg =
= 8Qb - (Qb^2)/6000 + 6Qg - (Qg^2)/6000
[the ^ symbol means "to the power of"]
The problem we have to solve is:
Max 8Qb - (Qb^2)/6000 + 6Qg - (Qg^2)/6000
Qb + Qg = 60,000
That is: choose how many tickets you want to sell to ...
Price as a function of Quantity is utilized in this case are determined. The marginal revenues in the two markets which must be equal are discussed.