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)
is:
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?

Solution Preview

Hello!
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

For girls:
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

subject to
Qb + Qg = 60,000

That is: choose how many tickets you want to sell to ...

Solution Summary

Price as a function of Quantity is utilized in this case.

... p = .04q + 8 and the demand function is p ... is found by setting equating the two functions equal to ... the resulting equation, giving the equilibrium price and the ...

... demand curve) until equilibrium is reached at a higher price, P2 and quantity, Q2 ... The rationing function of price is the change in market price to eliminate ...

... ionship between quantity produced and total costs. f production. p, we need to get more data points for wider range of output. tter cost function which can ...

... QD = 600-2P and the supply function stays the ... Find the new equilibrium price and quantity, and show ... By using given demand and supply functions, following table ...

... question the demand and supply functions have to ... solely determined by other variables in a function (quantity). ... by the other variables in a function (Price). ...

... (1)Find the firmÃ¢??s optimal quantity, price, and profit (1) by ... 1. The derivative of the total profit function gives us the point where profit is maximized. ...

... COMPETITVE MARKETFOR A CERTAIN SPICE, THE SUPPLY FUNCTION IS Qs ... (THE INVERSE SUPPLY AN DDEMAND FUNCTIONS ARE P ... B. THE EQUILIBRIUM PRICE IS $_____ PER POUND OF ...

... Graph these functions on the same axes. Also, find the equilibrium quantity and the equilibrium price. ... definition of the derivative to the function given below ...

... Show the demand curve with quantity expressed as a function of price, and price expressed as a function of quantity. ...price expressed as a function of quantity. ...

... Demand and supply functions for Florida orange juice are as follows: ... A. When quantity is expressed as a function of price, what are the Florida demand and ...