4. Examples

Assume that we wish to define a non-linear CES demand function for the aggregate demand TLPKM (passenger land travel), having the following component demands:

• TRT – passenger car travel

• TRB – passenger bus travel

• TRW – passenger two-wheeler travel

• TTP – passenger rail travel

The demand function can be set up with the following input parameters (where r stands for regions, t for milestone years, and ‘0’ for interpolation option placeholder):

Table 4.9 Non-linear CES demand function example.

Parameters	Description
COM_AGG(r,’0’,’TRT’,’TLPKM’) = 2;	Aggregation of TRT into TPASS with price ratios
COM_AGG(r,’0’,’TRB’,’TLPKM’) = 2;	Aggregation of TRB into TPASS with price ratios
COM_AGG(r,’0’,’TRW’,’TLPKM’) = 2;	Aggregation of TRW into TPASS with price ratios
COM_AGG(r,’0’,’TTP’,’TLPKM’) = 2;	Aggregation of TTP into TPASS with price ratios
COM_ELAST(r,t,’TLPKM’,’ANNUAL’,’FX’)=0.35;	Own-price elasticity of aggregate demand
COM_ELAST(r,t,’TLPKM’,’ANNUAL’,’N’)=1.2;	Elasticity of substitution between components
COM_VOC(r,t,’TLPKM’,’UP’)=1;	Max. upper variance of aggregate demand

Assume now that we wish to define the same demand function but with the linear formulation for the CES function. The demand function can be set up with the following input parameters (where r stands for regions, t for milestone years, and bd for the inequality bound types (‘LO’, ‘UP’)):

Table 4.10 Linear CES demand function example.

Parameters	Description
COM_AGG(r,’0’,’TRT’,’TLPKM’) = 2;	Aggregation of TRT into TPASS with price ratios
COM_AGG(r,’0’,’TRB’,’TLPKM’) = 2;	Aggregation of TRB into TPASS with price ratios
COM_AGG(r,’0’,’TRW’,’TLPKM’) = 2;	Aggregation of TRW into TPASS with price ratios
COM_AGG(r,’0’,’TTP’,’TLPKM’) = 2;	Aggregation of TTP into TPASS with price ratios
COM_ELAST(r,t,’TLPKM’,’ANNUAL’,’FX’)=0.35;	Own-price elasticity of aggregate demand
COM_ELAST(r,t,’TLPKM’,’ANNUAL’,’N’)=1.2;	Elasticity of substitution between components
COM_STEP(r,’TRT’,’FX’)=100;	Number of steps for TRT in both directions
COM_STEP(r,’TRB’,’FX’)=100;	Number of steps for TRB in both directions
COM_STEP(r,’TRW’,’FX’)=100;	Number of steps for TRW in both directions
COM_STEP(r,’TTP’,’FX’)=100;	Number of steps for TTP in both directions
COM_STEP(r,’TLPKM’,’LO’)=120;	Number of steps for TLPKM in lower direction
COM_STEP(r,’TLPKM’,’UP’)=80;	Number of steps for TLPKM in upper direction
COM_VOC(r,t,’TRT’,bd)=0.8;	Max. variance of TRT, given in both directions
COM_VOC(r,t,’TRB’,bd)=0.8;	Max. variance of TRB, given in both directions
COM_VOC(r,t,’TRW’,bd)=0.8;	Max. variance of TRW, given in both directions
COM_VOC(r,t,’TTP’,bd)=0.8;	Max. variance of TTP, given in both directions
COM_VOC(r,t,’TLPKM’,’LO’)=0.5;	Max. lower variance of aggregate demand
COM_VOC(r,t,’TLPKM’,’UP’)=0.3;	Max. upper variance of aggregate demand

Note that using ‘FX’ as a shortcut for bd={‘LO’,’UP’} in COM_STEP is only supported in TIMES v4.4.0 and above, and that COM_VOC does not have any such shortcut.