Question

1 The social cost of pollution

Steel production is a dirty business.It is a significant contributor to local air quality problems,

and it accounts for roughly 5% of greenhouse gas emissions globally. Two tons of carbon dioxide

are emitted for each single ton of steel produced. Despite efforts to innovate, there is no viable

technology for reducing the emissions intensity of steel production; the only way to reduce carbon

pollution in this industry is to reduce steel production.

Imagine that the steel market is characterized as follows

Marginal costs:MC(Q) = 1.25Q

Marginal benefits:MB(Q) = 27−Q

Marginal damages:MD(Q) = 0.25Q

(A) Draw a graph containing MC(Q),MB(Q), and, SMC(Q) =MC(Q) +(Q). Concisely

describe what each of these functions measure in the context of steel production and con-

sumption. [3 points]

Imagine that this market is perfectly competitive. Equilibrium steel production is then defined by

MC(Q∗) =MB(Q*).

(B) So what actually happens in this market, in equilibrium? I.e., what is (Q∗, P∗)? [2 points]

(C) Label (on a graph) and calculate the consumer surplus (CS), producer surplus (PS), and total

damages (TD). [3 points]

(D) What quantity (Q∗∗) maximizes total net benefits in this market? How do you know? Calcu-

late the deadweight loss in the market without any government intervention (i.e., (Q∗, P∗)).

[2 points]

(E) Explain how incentives in the free (i.e., no-intervention) market cause a deviation from the

outcome that would have maximized total net benefits. [2 points]

(F) Holding constant (P∗, Q∗), how would you expect Q∗∗to change if: (a) demand were more

inelastic; (b) marginal damages were larger? [2 points]

U.S. demand for steel is met by both domestic supply (≈70%) and imports (≈30%). The Trump

Administration implemented a tariff on all steel imports beginning in June of last year, with the

goal of supporting the domestic steel industry. One effect of this policy change was a higher price

of steel in the U.S. Imagine, for simplicity, that this price change was realized through an upward

shift in the marginal cost curve

MC1(Q) = 1.25Q+ 2.25

(G) Calculate the change in total damages caused by this shift in the marginal cost curve. [2

points]

(H) What percentage of the total lost surplus (CS+PS) from this change comes from a reduction

in consumer surplus? [2 points]

(I) Compare (in terms of magnitude) the ratio of the lost surpluses (∆CS/∆PS) to (the absolute value of) the ratio of the slopes (slopeD/slopeS)). [2 points]

Answer 1

A)

MB curve shows Marginal benefits, consumer are getting from consumption of steel.

MC curve shows Marginal cost of production for producers of production of steel.

MD curve shows Marginal damage cost that society has to bear for production of steel.

SMC curve shows aggregate marginal cost to society of production of the steel which is equal to MC + MD.

b)the competitive market equilibrium will be at where ,MB=MC{ ignoring MDC}

MB=27-Q

MC=1.25Q

MB=MC

27-Q=1.25Q

25=2.25Q

Q=27/2.25

Q* =12

P*/MB=27-Q=27-12=15

C)

CS=area of CS triangle=1/2*12*(27-15)=1/2*12*12=72

PS =area of PS triangle=1/2*12*(15-0)=1/2*12*12=72

MDC=0.25Q

TDC=0.125*Q^2{ using integration}

TDC=0.125*12*12=0.125*144=18

D) QUANTITY that will maximize net benefit is that,where SMC=MB

1.5Q=27-Q

2.5Q=27

Q**=10.8

Marginal damage cost at Q*=0.25Q=0.25*12=3

Difference between Q* and Q**=12-10.8=1.2

Deadweight loss=1/2*3*1.2=1.8

​​​