Question

1. The town of Springfield has two steel producers that pollute the air with Sulfur Dioxide (SO). Their supply curves are shown below, with quantities and kilotons and price per kilo. Producer + Producer B 2 . . . 10 12 # 16 Drano * 12 HM De a. Suppose the price of steel is $8/kho (demand is perfectly elastic). Draw the market supply curve and the equilibrium quantity of steel produced by the two factories. How much will each firm produce in equilibrium? IM social cost Supply Curve Hint: You can visually add the two supply curves to get the market supply, or you can do it algebraically by seeing that the two supply curves (expressed with Pon the left side) are P-Q and P-0/2. Then you add the two supply curves: QyQ,+Q, -P+2P 3P. So the market P=Qx/3 4 8 12 16 20 24 28 32 36 Total quantity 24 8 Assignment 4, p. 2 b. Now suppose Springfield decides that the pollution costs the people of Springfield $2 per kilo of steel produced. Note that the market supply curve corresponds to "private cost." Add the social cost" curve to the graph above. Show how and why the socially optimal total quantity of steel that the two firms should produce is What is the socially optimal production of each firm? Explain.
i need question b please

Answer 1

Initially we have, Supply of firem A : P = QA supply of firm B : P = QB Market Supply : P = pm 2 [Qm= QATQ The 'p' in represents the the supply equations private cost. aboue we know that, Social cost = priuate cost + cost of externality In our case externality is pollution and I the cost imposed by it is, $2 per Bilo of Steel So let Ps be the socially optimal price level, then we can write, ů Ps = P +2 [P→ Private cost - and Ps represents the the supply a social costen functions /

So based on i representing social o Ps = QA + 2 I opg = QB + 2 our supply functions cost will be, [Firma] [firm o] + 2 om A Pe = Qm+2 [market] At socially optimal point, market demand - Market Supply » 8 = Q m + 2 wo i bol » Qm - 6 2 jam = 18

- Put Om = 18 in Market Supply equation to get socially optimal price , Ps = Qm +2 Ps = 18 + 2 - Ps = 6+2=8 socially optimal output of firm A ii, Ps = QA+2 3 QA = P-238-2 = 6 socially optimal output of Firm B is, ' fs = @obe +2 - - QB = Ps-2 - - QB = 2(Ps-2) = 2(8-2) I mind that there will be no affect on market demand . It will be Same 1 as before ice R28. _ = 12