Perhaps better suited for another Stack Exchange community, but I'm confused on three different economics terms and seek clarification. The terms are "Demand Curve, "Price Response Function", and "Willingness to Pay".
I had thought that the demand curve was a classic sigmoid function where the X-axis represents price and the Y-axis represents probability of an arbitrary consumer purchasing the product.
Yet, when I dug into the demand curve, I saw something different. The Y-axis represented the price, and the X-axis represented the number of units demanded.
Could someone clarify what each of these terms mean mathematically and where did I go right/wrong?
You are describing two different functions when talking about the demand function.
The demand function, in which the $y$-axis represents the price of the commodity and the $x$-axis represents the quantity of the commodity that is demanded at that price.
The inverse demand function, which represents price as a function of quantity. As an inverse function, the $y$-axis will now represent the quantity and the $x$-axis the price.
Now, the willingness to pay is the maximum price at or below which a buyer will buy one unit of a product.
The price response function describes demand for the product of a single seller.