There are three consumers of a public good. The marginal willingness-to-pay for
ID: 2496507 • Letter: T
Question
There are three consumers of a public good. The marginal willingness-to-pay for the consumers are as follows:
consumer 1 :MWP1(Q)=60-Q
Consumer 2: MWP2(Q)=100-Q
consumer 3: MWP(Q)=140-Q
Where MWPi (i=1,2,3) is in dollars per unit and Q is the quantity of the public good. The marginal cost of the public good is $180. a) What is the efficient level of production of the public good? b) If the three consumers were to pay a third of the cost of producing the public good, what quantity of the public good would be produced? What would be the size of the deadweight loss? c) Propose an alternative cost sharing arrangement that leads to the efficient quantity of the public good being produced.
Explanation / Answer
a) The economically efficient level of output occurs where MSB = MC .
So (60-Q) + (100-Q) + (140-Q) = 180
300-3Q = 180
3Q = 120
Q = 120 / 3 = 40
b) If the cost reduced to 180 / 3 = 60
When marginal cost is MC 60 , the MSB and MC curves intersect at a level of output at which only consumers 2 and 3 have a positive willingness to pay. This implies the efficient level of production will occur where
(100-Q) + (140-Q) = 60
240-2Q = 60
2Q = 180
Q = 180 / 2 = 90
c) If the good is not provided at all, the deadweight loss would be the area under the the MSB curve and above the marginal cost curve, or 0.5(300 – 180)(40) = 2400. This is a deadweight loss because it measures the potential net economic benefits that would disappear if the good were not offered.
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