Quick start - Gams

The economic equilibrium model was of the form
Demand Price: P > Pd = 6 - 0.3*Qd
Supply Price: P < Ps = 1 + 0.2*Qs
Quantity Equilibrium: Qs > Qd
Non negativity P, Qs, Qd > 0
and is a single commodity model. Introduction of multiple commodities means that we need a
subscript for commodities and consideration of cross commodity terms in the functions. Such a
formulation where c depicts commodity can be presented as
Demand Price for c: Pc ≥ Pd c = Idc
- ∑Sd
c, cc * Qd cc for all c
Supply Price for c: Pc ≤ Ps c = Isc
+ ∑Ss
c, cc * Qscc
for all c
Qsc ≥ Qd c
Quantity Equil. for c: for all c
Pc , Qd c , Qsc
Non negativity for all c
≥
where Pc is the price of commodity c
Qdc is the quantity demanded of commodity c
Pdc is the price from the inverse demand curve for commodity c
Qsc is the quantity supplied of commodity c
Psc is the price from the inverse supply curve for commodity c
cc is an alternative index to the commodities and is equivalent to c
Idc is the inverse demand curve intercept for c
Ddc,cc is the inverse demand curve slope for the effect of buying one unit of commodity
cc on the demand price of commodity c. When c=cc this is an own commodity
effect and when c≠cc then this is a cross commodity effect.
Isc is the inverse supply curve intercept for c
Dsc,cc is the inverse supply curve slope for the effect of supplying one unit of commodity
cc on the supply price of commodity c. When c=cc this is an own commodity effect
and when c≠cc then this is a cross commodity effect.
An algebraic based GAMS formulation of this is (econequilalg.gms)
Set commodities /corn,wheat/;
Set curvetype /Supply,demand/;
Table intercepts(curvetype,commodities)
corn wheat
demand 4 8
supply 1 2;
table slopes(curvetype,commodities,commodities)
corn wheat
demand.corn -.3 -.1
demand.wheat -.07 -.4
supply.corn .5 .1
supply.wheat .1 .3 ;
Courtesy of B.A. McCarl, October 2002 26
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