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

AI Thread Summary
The discussion centers on the dimensional correctness of the demand function y=5000-p, highlighting that it lacks proper units. An implicit coefficient of 1.0 unit-of-price^-1 is necessary for dimensional accuracy. The conversation explores how to express price and quantity in compatible units, such as liters of water and dollars. Participants suggest that the unit of demand might be a dimensionless number or defined in specific terms like 1000 items. The importance of aligning dimensions in economic equations is emphasized for clarity and correctness.
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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?
 
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Alexmahone said:
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 $$1.0 \text{ unit-of-price}^{-1}$$, which will make it dimensionally correct.
 
I like Serena said:
Hi Alexmahone,

There's an implicit coefficient of $p$ that is apparently chosen to be $$1.0 \text{ unit-of-price}^{-1}$$, 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

[math]\frac{y}{1\text{ litre of water}}=5000-\frac{p}{$1}[/math]
 
Last edited:
Alexmahone said:
Is this what you mean?

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

[math]\frac{y}{1\text{ litre of water}}=5000-\frac{p}{$1}[/math]

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:
$$y=5000 \text{ kItems} - 1 \frac{\text{kItems}}{10\text{ k}\$} \cdot p$$
 
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