Unit Error: Mantissa of ^ must be dimensionless

[Ginarley]

Hi all

I am not sure how to fix this units error which comes about when trying to recreate the Agrarian society model from chapter 3 of Hannon & Ruth's Dynamic Modelling (1994). The model is essentially a basic population model with a cobb-douglas production function tacked on to produce tools from labour and another to produce food from both tools and labour. The model runs fine and behaves sensibly but running the units check I get the following two unit errors and I don't know what it means or how to resolve it:


************************************************
Error in units for the following equation:
Food Production =
Total Food Productivity Factor
* Population
^ Food Elasticity of Labour
* Tools
^ Food Elasticity of Capital
Food Production --> Food/Year
Total Food Productivity Factor --> Food/(Year*Person*Tool)
Population --> Person
Food Elasticity of Labour --> Dmnl
Tools --> Tool
Food Elasticity of Capital --> Dmnl

Analysis of units error:
Mantissa of ^ must be dimensionless
Population
Has Units: Person

***********************************************
Error in units for the following equation:
Manufacturing =
Total Tools Productivity Factor
* Population
^ Tool Elasticty of Labour
Manufacturing --> Tool/Year
Total Tools Productivity Factor --> Tool/(Year*Person)
Population --> Person
Tool Elasticty of Labour --> Dmnl

Analysis of units error:
Mantissa of ^ must be dimensionless
Population
Has Units: Person
***********************************************

Any suggestions would be very much appreciated.

Cheers
Ginarley

[karankhosla]

I would introduce the following "unit factors" (see unit description below):

Food Production =
Total Food Productivity Factor*(Unit Population*Unit Tools)
* (Population/Unit Population)
^ Food Elasticity of Labour
* (Tools/Unit Tools)
^ Food Elasticity of Capital

Food Production --> Food/Year
Total Food Productivity Factor --> Food/(Year*Person*Tool)
Population --> Person
Unit Population [value=1] -->Person
Food Elasticity of Labour --> Dmnl
Tools --> Tool
Unit Tools [value=1] --> Tool
Food Elasticity of Capital --> Dmnl

[Edited on 10-5-2010 by karankhosla]

[bob@vensim.com]

The standard SD formulation for the Cobb-Douglas production function is

output = reference output * (input 1/reference input 1)^factor 1 *
(input 2/reference input 2)^factor 2

and so on where factor n is Dmnl and reference output has the same units as output. Reference inputs and outputs are either nominal, or more usefully selected from around an initial or average operating point. eg reference workforce might have the same value as initial workforce in the model.

[tomfid]

Sometimes, for transparency, it's good to take Bob's equation and break it out into several, for example:

output = reference output * effect of factor 1 * effect of factor 2
effect of factor 1 = (input 1/reference input 1)^factor 1
effect of factor 2 = (input 2/reference input 2)^factor 2