ISIS-Cement Import Modeling 

Meeting with the Portland Cement Association (PCA) 

Portland Cement Association and constituents joined EPA over the phone 

Tyrone Wilson 

Ed Sullivan 

Tian Lu 

Stu Sessions 

Doug Roark 

Bob- contractor with PCA 

EPA 

Elineth Torres 

Ravi Srivastava 

Contractor to EPA

Samudra Vijay- Sam Analytic Solutions LLC – over the phone 

Topics for discussion 

Imports 

o Ravi Srivastava explained that Dallas Burtraw with Resources for the Future 

(RFF) econometrically determined the elasticity of cement imports to be 3.94. 

For his analysis Dallas used USGS data. Import data was aggregated for 5 

countries and the rest of the world- using the c.i.f- custom price. More 

information to be found in the memo from Dallas to EPA. 

o Ed commented that the current function underestimate the cost of imports and 

underestimate the welfare. The cost of imports relates to the freight rate per 

custom district and this is a function of oil prices which relates to demand of 

ships. Per Ed, a correlation of freight prices and oil prices is needed to augment 

the import function in ISIS. 

o Ravi- proceeded to present to PCA the main equations of ISIS-cement. 

Objective FunctionConstraintImports 

Domestic side 

Economic welfareSupply 

Imports 

Domestic side 
CalibrationNew methodology for calibration will capture a horizon of 4 to 5 years 

(2004-2009) - match the historical quantities and see how the model 

behaves. Calibration 

Stu agreed that the calibration should account for a time horizon of multiple years. 

We will follow-up this meeting with a call with Dallas Burtraw from RFF on March 18 

2010. 

Model key Equations discussed with PCA 

Objective Function 

Total surplus = area under the demand curve – area under the supply curve 

The objective is to maximize total surplus, or minimize the negative of total surplus. 

Then, 

Minimize z = ∑ ∑ ∑ (1) 

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ − +− ++ t = =

j k DP IP cc tc)(I pc)(D

l

1j

k

h

1j

j

where, 

Dj = demand quantity (tons) in the j

th slice of the demand-price curve in year t

P(Dj) = cement price ($/ton) corresponding to Dj

pc = production cost ($) in year t 

Ik = import quantity (tons) in the k

th slice of the imports-price curve in year t

P(Ik) = cement price ($/ton) corresponding to Ik

tc = transportation cost ($) in year t 

cc = control costs ($) in year t 

σ

1

0

0 )( ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = D

D

PDP j

j

λ

1

0

0 )( ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = I

I PIP k

k
σ and λ are elasticities of demand and imports relative to price 

Note that in (1), the area under the demand curve is approximated by adding areas of h

equal segments with j denoting the j

th segment. A similar procedure is followed for the 

imports term. 

Supply Constraint 

prodn(t) + I(t) >= D(t) (2)

where, 

prodn(t) = quantity (tons) produced domestically in year t 

I(t) = quantity (tons) imported in year t, and 

D(t) = demand(tons) for the commodity in year t. 

Emissions Constraint 

ISIS framework can accommodate several different types of emissions constraints (e.g., 

cap-and-trade, emission limits). 

For example, in the case of cap-and-trade, 

em(t) = ec(t) + bnk (t) – bnk (t+1) (3)

where, 

em(t) = industry emissions (tons) of a given pollutant in year t, 

ec(t) = emissions cap (tons) in year t, 

bank (t) = banked allowances in year t, 

 bank (t+1) = banked allowances in year t+1.