Basically, On my University forums, we've had a debate, about the fundamentals of supply (First semester, at Sydney Uni.)
In order to create a sloped non-linear (both not straight and not with a constant velocity or acceleration) graph "/" you must use two variables. One being the X and one being the Y.
The Y is price, and the X is quantity.
However while the demand for quantity is given as "the quantity demanded at this exact particular point in time."
The nature of supply is abit different, because it involves business estimating the supply at each given price level. This is because they cannot know for sure, how much they can supply at each given price point (unknown costs in expanding production etc etc.)
This is basically the nature of my argument. In that if you hold "business expectations" constant, you will end up with a vertical supply line. And that by factoring in "business expectations" as a Variable you will gain the traditional Marshallian sloped supply line.
I used alot of austrian sources in the argument, namely Klein, and Salerno. Just want to make sure my approach is actually consistent with the Austrian method.
So incase you find my writing abit difficult to understand. The question is, is it possible to hold "business expectations constant" while constructing a (non-vertical) supply graph?
Since you define the "demand for" quantity is given as "the quantity demanded at this exact particular point in time.", you should define the "supply of" quantity as "the quantity supplied at this exact particular point in time." In this case, both are unknown, but can be approximated by a number of methods.
Its impossible, to supply infinite combinations of a good at any point in time. the supply graph is thus an Estimation of the future.
demand = Ex post
Supply = Ex ante
There is an inverse relationship between price and quantity demanded. If the price goes up, the quantity demanded goes down (but demand itself stays the same). If the price decreases, the quantity demanded increases (but again demand stays the same). On a graph, an inverse relationship is represented by a downward sloping line from left to right.