Matching LHS-RHS units in equation that has Power function

[SVK]

I am Vensim PLE (version 6.3D). I am currently using Vensim to model Solow's economic model.

A key function in the Solow model is a production function (Cobb Douglas equation) described below:

Y(t) = Alpha∗A∗Power(K,Alpha)∗Power(P,1−Alpha) where Y(t) is total income (unit: Money/Year), Alpha is the ratio of capital income to total income (ideally, unit:dimensionless), K is the firm capital (ideally, unit: "Money"), P is the total labor (ideally, Person/Year) and A the technology multiplier (ideally, dimensionless).

I modeled the above equation in Vensim using normalized values of firm capital and total labor (i.e. firm capital and total labor have been kept as dimensionless). This works & passes unit check. But if I do not use normalized values, I am not able to get a correct unit for income Y(t), which is Money/Year.

Is there a way to avoid using dimensionless variables and still retain the "real" units of the equation's constituents ?

[tomfid]

The terms in the equation should be normalized by reference values of output, capital and labor, like:

Y/Y0 = A * (K/K0)^alpha * (L/L0)^(1-alpha)
so
Y = A * Y0 * (K/K0)^alpha * (L/L0)^(1-alpha)

Then all the bases of the exponents will be dimensionless, and it's typically easier to initialize the function around some point.

[SVK]

Many thanks for the reply. Is there a way in Vensim to use units directly inside a Vensim equation ? For example, I have "Person" as a unit in the model. Will it be possible to enhance existing equation as follows:
Modified equation => (Existing equation) * 1/Person

[Administrator]

Many thanks for the reply. Is there a way in Vensim to use units directly inside a Vensim equation ? For example, I have "Person" as a unit in the model. Will it be possible to enhance existing equation as follows:
Modified equation => (Existing equation) * 1/Person

No. This is not something we would implement in Vensim.

But there is nothing to stop you creating a variable called "person", with the unit "person".

[tomfid]

There's a reason for this incidentally. Numbers in an equation that have dimensions are often implicit parameters that should be exposed to scrutiny and testing.

Admittedly, the number of meters in a kilometer is not up for discussion. For conversion factors like that, you can set the "unchangeable" subtype.