Question

The London Met. Police must decide how to allocate police officers between East London and Centre City. Measured in arrests per hour, the average product, total product, and marginal product in each of these two areas are given in the table below. Currently the police allocate 200 police officers to Centre City and 300 to East London. If police can be redeployed only in groups of 100, how, if at all, should the police reallocate its officers to achieve the maximum number of arrests per hour?

City Centre East London Number of police AP TP MP AP TP MP 375 48 100 75 75 75 48 48 75 40 200 150 44 88 75 32 300 75 225 40 120 75 24 400 75 300 375 36 144 75 170 500 75 34 26

Answer 1

Currently 300 police are deployed in East London and 200 in City centre. Hence the aggregate TP = 225 + 88 = 313. The scenario is given below:

East London Number of Police MP ol AP TPMP 0 0 75 75 75 75 150 7 5 75 225 75 75300 75 7 5 375 75 100 200 300 400 500 City Center AP TP 0 0 4848 44 88 40 120 36 144 34 170 48 40

Since there are 500 police and they need to be reallocated to maximize total product. They can be redeployed only in groups of 100. Hence, the possible combinations would be 0-500, 100-400, 200-300, 300-200, 400-100 and 500-100 among East London and City Center as shown below. TP_Eat London and TP_City Centre are fetched from the above information corresponding to the number of police deployed. Aggregate TP sums up the TP from deployment of police in both location. It can be observed that aggregate TP is highest when all 500 police are deployed in East London and none in City Centre. This has been highlighted in green.

75 East London City Center TP East London TP City Center Aggregate TP 500 170 170 100 400 144 219 2001 300 150 120 270 300 200 225 313 400 100 300 348 500 375 O 88 375