Question

the bank is charging flat fee of 10 per car to park at rhe lot and there are hunderd space and lot is open from 6 pm to midnivht every night and is staffed by a single employee the employee is pad 10 per hour   .the bank has indiactaed that maintenance cost   are insignificant . identify the marginal revenue and marginal cost for each additional care thats oays to use the banks parking lot and exolain why the bank is able to set the fees as high as in contrast when the parking lot is available at all times

Answer 1

Fees per car = 10

No. Of cars that can be parked = 100

Staff is comprised of only one employee who is paid 10 per hour.

Therefore, total cost pertaining to 6 hours (from 6pm to 12 midnight) = 6*10= 60

Maintenance cost = 0

Since, MR = d/dx of Total revenue (TR) and MC= d/dx of Total cost(TC).

TR= 10*x ; where x = number of cars parked

TC( total cost) = 10*6= 60

Therefore Marginal Revenue (MR) = d/dx (10x) = 10

Marginal cost (MC) = d/dx (60) = 0

The bank is able to charge a high fee as in contrast when the parking lot is available at all times because the cost pertaining to 6 hours of availability is very low and staff consists of only one employee. Had the parking been available for 24 hours, the variable cost and hence the marginal cost (more employees) would have been higher and it will be an increasing function. But in this case the marginal cost is 0 and therefore the bank is able to charge as high fees as possible since MR=MC(0). Had the bank been available for parking at all times, the Marginal cost might have been positive due to which the price might have been lesser.