Answer to Question #240225 in Macroeconomics for Fauzi

Question

Britney and Paris are neighbors. During the winter, it is impossible for a snowplow to clear the street in front of Britney's house without clearing the front of Paris's. Britney's marginal benefit from snowplowing services is 12 − Z, where Z is the number of times the street is plowed. Paris's marginal benefit is 8 − 2Z. The marginal cost of getting the street plowed is $16. Sketch the two marginal benefit schedules and the aggregate marginal benefit schedule. Draw in the marginal cost schedule, and find the efficient level of provision for snowplowing services.

Answer 1

The marginal benefit from ploughing service for both individuals is given as follows.

$MB_B=12-z\\MB_P=8-2z$

Total marginal benefit

$MB_A=MB_B+MB_P\\=12-z+8-2z\\=20-3z,z<4$

Equating $MB_A=MC$

$20-3z=16\\4=3z\\z=1.33$

therefore the efficient level of snowplowing is i.33

If either Britney or Paris had to pay for the entire service themselves, no plowing would have occurred since the marginal cost of $16 exceeds either of their individual marginal benefits from the first unit ($12 or $8 ).