CarbonTrading:WhiteCementInc. (Reference Online Case by Harvard Business School

AstheproductionmanagerforWhiteCementInc.,youarefacingplanningchoicesforthenextfiscal year.Inaddition to thenormal costs of production foryour operation, yourcompanynow faces

anewcost:paymentforpermitstoproducethepollutionthatisabyproductofthecement

manufacturing process. Your company produces carbon dioxide in levels proportional to the amountof cement you produce. For every ton of carbon dioxide (CO2) you emit, you must submit to theCouncil On Undesirable Gaseous Hazards (COUGH) one Carbon Allowance (CA) - a 'permit' to emitthatton of pollution.

Your company's cost and pricing structures are as follows.Each year, you may choose to producequantityQofyourproduct-rawcement-measuredinthousandsoftons.Thepriceatwhichyoucan sell this quantity is given by the equation P(Q) = 200-2Q, where price is measured in dollars perthousand tons. Your costs ofproduction are linear: producing Q(measured in thousands of tons)costs5Q.Therefore,yourgrossprofitatproductionlevelQwillbeQ*P-5Q,or(Q*(200-2Q)-5Q).

Beginning this year, pollution permits will enter the cost structure. For every thousand tons ofcement you produce, your factories emit2 tons ofcarbon dioxide. If you choose, you can reduce thisratebypaying$1000toinstallanewlyavailablecleanmanufacturingtechnology.Thistechnologywill reduce your emissions to a rate of 1.5 tons of carbon dioxide per thousand tons of cement.

At theend of the year, you must submit permits corresponding to your level of pollution, or else you aresubject to a penalty of $40 per ton of CO2. Based on historical production levels at your firm, COUGHhas granted you 150 permits. Should your production exceed this level, you will be required to buyadditionalpermits, orelsefacepenalties.

The price of carbon permits is not fixed. Rather, it is determined on the open market based on thepermit needs of other regulated polluters.

There are four other companies competing for permits inthis market. While you don't know the permit needs of these companies, you do know that in total,190 permits have been allocated among them. These permits, along with your own, constitute allavailable permits. That is, 340 represents a cap on permits outstanding - and hence allowed pollutionlevels. So in addition to choosing your production level, you may trade with your competitors, eitherbuyingpermitstomeetyourneeds,orsellingpermitsshouldyouhavea surplus.

Theyearoftradingwillberepresentedbya21minuteperiod.Youmaytradepermitswithyour competitorsthroughouttheentireperiod. Atthe7-minutemark, youmust decidewhetherto purchase and install clean technology. At the 14-minute mark, you must lock in your productionquantity for the year. At the 21 minute mark, the market is closed. All permits are submitted and youmustpayafineof$40pertonof pollutionthat exceedsyour permitholdings.

CleanTechnology Lock inProduction

7minutes(Trading)

7minutes(Trading)

7minutes(Trading)

i) Assume that you choose not to have clean technology. What production quantity would you pick?

ii) Assume that you choose to have clean technology. What production quantity would you pick?

iii)How would your answers depend on the price of carbon permits?

How do you approach the above problem? Is there a standard way of calculating?

Note: This is a case sheet 9-911-055 dated FEBRUARY25,2011 and I need the approach to this problem.