A private-garage owner has identified two distinct market segments: short-term parkers and all-day parkers with respective demand curves of Ps = 3 - (Qs/200) and Pc = 2- (Qc/200). Here P is the average hourly rate and Q is the number of cars parked at this price. The garage owner is considering charging different prices (on a per-hour basis) for short-term parking and all-day parking. The capacity of the garage is 600 cars, and the cost associated with adding extra cars in the garage (up to this limit) is negligible.
a.) Given these facts, what is the owner�s appropriate objective? How can he ensure that members of each market segment effectively pay a different hourly price?
b.) What price should he charge for each type of parker? How many of each type of parker will use the garage at these prices? Will the garage be full?
c.) Answer the questions in part b.) assuming the garage capacity is 400 cars.
a) The garage owner's appropriate objective is to maximize profit. To ensure that members of each market segment effectively pay a different hourly price, the owner can implement price discrimination. This means charging different prices to different segments of customers based on their willingness to pay.
b) To determine the price and quantity for each type of parker, we need to find the equilibrium point for each demand curve.
For short-term parkers (Ps), the demand equation is:
Ps = 3 - (Qs/200)
For all-day parkers (Pc), the demand equation is:
Pc = 2 - (Qc/200)
To find the equilibrium price and quantity for short-term parkers, we set the quantity supplied (Qs) equal to the quantity demanded (Qs), and solve for Ps:
Qs = 600 - Qc (since the capacity of the garage is 600 cars)
Ps = 3 - (Qs/200)
Substituting Qs = 600 - Qc into the demand equation for Ps:
Ps = 3 - ((600 - Qc)/200) (Equation 1)
To find the equilibrium price and quantity for all-day parkers, we set the quantity supplied (Qc) equal to the quantity demanded (Qc), and solve for Pc:
Qc = 600 - Qs (since the capacity of the garage is 600 cars)
Pc = 2 - (Qc/200)
Substituting Qc = 600 - Qs into the demand equation for Pc:
Pc = 2 - ((600 - Qs)/200) (Equation 2)
Now, we can solve equations 1 and 2 simultaneously to find the equilibrium prices (Ps and Pc) and quantities (Qs and Qc) for each type of parker.
c) To answer the questions in part b) assuming the garage capacity is 400 cars, you would follow the same process as in part b), but with the quantity constraint changed to Qs + Qc = 400 instead of 600. This means the total number of cars that can be parked in the garage is 400 instead of 600.
Repeat the steps in part b) using the modified quantity constraint of Qs + Qc = 400 to find the equilibrium prices and quantities for each type of parker.