Is there a correct way to include dimensions in economics equations?

[alexmahone]

A typical demand function is y=5000-p where y is quantity demanded and p is price. But this equation isn't dimensionally correct. What am I missing?

 

[I like Serena]

A typical demand function is y=5000-p where y is quantity demanded and p is price. But this equation isn't dimensionally correct. What am I missing?

Hi Alexmahone,

There's an implicit coefficient of $p$ that is apparently chosen to be \(\displaystyle 1.0 \text{ unit-of-price}^{-1}\), which will make it dimensionally correct.

 

[alexmahone]

Hi Alexmahone,

There's an implicit coefficient of $p$ that is apparently chosen to be \(\displaystyle 1.0 \text{ unit-of-price}^{-1}\), which will make it dimensionally correct.

Is this what you mean?

Assuming that price is to be measured in \$, and output in litres of water, the equation would be

\(\displaystyle \frac{y}{1\text{ litre of water}}=5000-\frac{p}{$1}\)

 

[I like Serena]

Is this what you mean?

Assuming that price is to be measured in \$, and output in litres of water, the equation would be

\(\displaystyle \frac{y}{1\text{ litre of water}}=5000-\frac{p}{$1}\)

Basically, yes.
I actually left out the unit of demand, which is presumably a dimensionless number.

Then again, suppose the unit of demand is 1000 items and the unit of price is 10000 \$, then the formula would be:
$$y=5000 \text{ kItems} - 1 \frac{\text{kItems}}{10\text{ k}\$} \cdot p$$