Scenario: Private and External Benefits A small community finds that tidy lawns

Question

Scenario: Private and External Benefits
A small community finds that tidy lawns and neighborhoods provide both private and external benefits. They determine the marginal private benefit (MPB) of lawns can be represented by the following equation: MPB = 50 – 0.5Q, where Q is the number of hours spent on keeping lawns tidy. The marginal private cost (MPC) of such lawn upkeep is represented by the following equation: MPC = 0.5Q, where Q is again the number of hours engaged in lawn upkeep.
Reference: Ref 17-19

(Scenario: Private and External Benefits) Based on the information provided, how many hours of lawn upkeep will occur in this community, and what will the marginal private benefit be of such upkeep?
Choose one answer.
a. 50 hours; $25
b. 45 hours; $20
c. 50 hours; $50
d. 100 hours; $50

Explanation / Answer

a. 50 hours; $25

Optimum allocation is done when MPB= MPC

MPB= 50 - 0.5Q

MPC= 0.5Q

MPB= MPC

50 - 0.5Q=  0.5Q

0.5Q+0.5Q=50

Q=50 ,

So number of lawn hrs is 50 hrs.

When this is substituted in the MPB we get the marginal private benifit.

MPB= 50 - 0.5 (50)

      = 50- 25

     = $25

So, lawn hrs is 50 and MPB is $25

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