A firm produces electricity from a coal fired furnace with marginal cost function of MC= 4+2q, where q is the amount of electricity produced. There are adverse health and environmental costs from burning coal. you do a study and find that each unit of electricity produced form coal leads to $1 worth of heath costs to society and $.50 of other environmental costs to society.
a) what is the formal for marginal private cost?
b)what is the formula for marginal external cost?
c) what is the formula for marginal social cost?
d) is the firm produces 10 units of electricity what is the total social cost?
(a) Marginal Private Cost is the cost firm incurred in order to produce one additional electricity from coal. Hence, Marginal Private Cost = MC = 4 + 2q
=> Marginal Private Cost = 4 + 2q
(b) Marginal External Cost is the cost of negative externality that firm creates to the society in order to produce one additional good. Hence,
Marginal Social Cost = health cost per unit + environmental cost per unit
= 1 + 0.5 = 1.5
Hence, Marginal External Cost = $1.5
Marginal Social Cost = Marginal Private Cost + Marginal External Cost
= 4 + 2q + 1.5 = 5.5 + 2q
=> Marginal Social Cost = 5.5 + 2q
(d) Total social cost for producing 10 units is the sum of all marginal social cost till producing 10 units
=> Total social cost = 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24 + 1.5*10 = $169
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