In: Economics
Kip’s Auto Detailing has locations in two distant neighborhoods, Uptown and Downtown. Uptown customers’ demand is given by QUT=1,000−10PQUT=1,000−10P, where Q is the number of cars detailed per month; Downtown customers’ demand is QDT=1,600−20PQDT=1,600−20P. The marginal and average cost of detailing a car is constant at $20.
a. Determine the price that maximizes Kip’s profit if he prices uniformly in both markets. How many customers will he serve at each location? What are his total profits?
P = $
QUT =
customers
QDT =
customers
Profit = $
b. Suppose Kip decides to charge different prices at each location. What price should he establish in each location? What are his total profits?
PUT = $
PDT = $
Profit = $
c. How big are the gains to Kip’s differential pricing scheme?
$333.66
$999.33
$666.66
$500.33