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Fuji is the sole manufacturer of racing bikes, and the cost of manufacturing is TC(Q)=120+15Q+2Q2TC(Q)=120+15Q+2Q2 so that the marginal cost is MC(Q)=15+4QMC(Q)=15+4Q
Fuji is the sole manufacturer of racing bikes, and the cost of manufacturing is TC(Q)=120+15Q+2Q2TC(Q)=120+15Q+2Q2 so that the marginal cost is MC(Q)=15+4QMC(Q)=15+4Q. Demand for racing bikes is characterized by P=132−4QP=132−4Q.
a. What is the optimal level of production and price for Fuji?
b. The production of the bikes produces pollution so that the additional externality cost is MCEX(Q)=5+4QMCEX(Q)=5+4Q. What is the social marginal cost of production of bikes?
c. What would be the social optimal level of production?
Expert Solution
Given that;
TC=120+15Q+2Q2MC=15+4QP=132−4QTC=120+15Q+2Q2MC=15+4QP=132−4Q
a).
The optimal level of production occurs at a point where the demand curve is equal to the supply curve (marginal cost curve above the minimum average variable cost):
15+4Q=132−4QQ=14.63P=$73.4815+4Q=132−4QQ=14.63P=$73.48
The optimal output and price are 14.63 units and $73.48, respectively.
b).
The social marginal cost (SMC) is equal to marginal private cost (MPC) plus external cost (E):
MSC=MPC+E=15+4Q+5+4Q=20+8QMSC=20+8QMSC=MPC+E=15+4Q+5+4Q=20+8QMSC=20+8Q
The marginal social cost is 20+8Q.
c).
The social optimal level of production occurs at a point where the marginal social cost is equal to the demand curve:
MSC=D20+8Q=132−4QQ=9.33P=$94.68MSC=D20+8Q=132−4QQ=9.33P=$94.68
The social optimal level is 9.33 units, each at $94.68.
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