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# HW_S1 - 1.You are the counselor to the governor Now your...

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1.You are the counselor to the governor. Now your task is to decide whether the following industry needs to be regulated. This competitive industry producing a certain chemical fertilizer in California faces the inverse demand P=100-30Q. The marginal private cost of the industry is 20+10Q. (a) Determine algebraically and graphically the competitive quantity and price. The competitive equilibrium is achieved where demand equals supply or when MPB=MPC for the industry. MPB=inverse demand=100-30Q MPC=supply=20+10Q MPB=MPC a Q =2, 40 a P = Figure 1. Graph for part (a) (b) The production of the fertilizer is associated with an externality environmental cost 5+5Q. Given this information, suppose you are employed by the California government to maximize the social welfare, what is the optimal quantity that maximizes social welfare? What is the market price now? What are the CS, PS, TEC (total externality cost), and SW under this pair of price and quantity? The social optimal outcome is achieved where MSB=MSC MSB=MPB=100-30Q MSC=MPC+MEC=20+10Q+5+5Q

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MSB=MSC 5/3 b Q = , 100 30 50 b b P Q = - = Figure 2. Graph for part (b) Let us call the P-intercept of MPB at 100 as Z. CS(Qb)=The triangular area below MPB and above Pb=triangular ZEPb = 0.5*(100-Pb)*Qb=125/3 PS(Qb)=the trapezoid PbEBA= 0.5*[Pb-20+(Pb-MPC(Qb))]Qb =36.11 TEC(Qb)=the trapezoid OCDQb=0.5*Qb*(5+MEC(Qb))=15,278 SW(Qb)=SB-SC=ZEQbO-FEQbO=ZEF=0.5*(100-25)*Qb=62.5 (c) Now a new science discovery found that when farmers apply this fertilizer in their orchard, honey bees in the area will become more productive. This marginal external benefit is estimated to be 10+10Q. The governor asks you to take this new piece of information into account when you report to him. Now what is the social optimal price and quantity? What are the CS, PS, TEB (total externality benefit), TEC and SW now?
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