Given the following cost function
P1=210-5Q1
P2=125-1.25Q2
TC=4000+20Q where Q=Q1+Q2
Required
a) calculate the profit maximizing quantity
b) compute the number of passengers who should pay at the high rates for the conductor to maximize profit.what should be the high rates
a) The profit maximizing quantity is found by setting the marginal revenue equal to the marginal cost.
MR1 = 210 - 10Q1
MR2 = 125 - 2.5Q2
MC = 20
Setting MR1 = MC, we get Q1 = 10.5.
Setting MR2 = MC, we get Q2 = 5.
Therefore, the profit maximizing quantity is Q = 10.5 + 5 = 15.5.
b) The number of passengers who should pay at the high rates for the conductor to maximize profit is 10.5. The high rates should be $210 - 10.5Q = $105.