Suppose Phillips and Mathew are the only tenants in a building. The owner of the building is considering installing surveillance cameras in the building
The following table shows the amount that Phillips and Mathew are willing to pay for each additional camera:
Number of Surveillance Cameras Phillips's Willingness
to Pay Mathew's Willingness to Pay
1 $400 $300
2 $310 $200
3 $210 $110
4 $80 $30
If the cost of installing each surveillance camera is $320, how many cameras will the owner of the building install to maximize welfare?
The owner of the building will continue installing cameras until the marginal cost of installing an additional camera equals the marginal benefit from its installation. The marginal benefit from the installation of a camera can be estimated from the total willingness to pay for an additional camera. Thus, the owner will continue installing cameras as long as the total willingness to pay for a camera exceeds the marginal cost. The total willingness to pay for the first surveillance camera is $400 + $300 or $700, which exceeds the marginal cost of $320. Therefore, the first camera will be installed. The total willingness to pay for the second camera is $310 + $200 or $510. Therefore, the second camera will also be installed. The total willingness to pay for the third camera is $210 + $110 or $320 which equals the marginal cost. Therefore, the third camera will also be installed. Because the total willingness to pay for the fourth camera is lower than the marginal cost, only 3 cameras will be installed.
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