Assume the demand curve is given by:
\begin{equation}
s = s_0 \left ( 1 - \frac{p}{p_0} \right )
\end{equation}
Where \begin{equation}p_0\end{equation} is the price at which noone will buy the product, and \begin{equation}s_0\end{equation} is the quantity that can be given away for free.
My thought is that the production curve is proportional to the number of workers in the industry and their productivity.
\begin{equation}
s = \frac{w}{h}
\end{equation}
where w = # workers, and h = hours per worker per unit.
The only missing element is the wage of the worker: c. But assuming the price covers all labor costs (in the abstract sense of the word), then it must be then that the price is roughly equal to the number of hours of labor per unit times the cost of that labor time.
\begin{equation}
p = hc
\end{equation}
Combining with the above, and solving for the number of workers in the industry (assuming wages don't change significantly).
\begin{equation}
w = h s_0 \left ( 1 - \frac{hc}{p_0} \right )
\end{equation}
This is a quadratic function of the labor time, with a maximum value at
\begin{equation}
h = \frac{p_0}{2 c}
\end{equation}
My interpretation of this equation and the story it tells is as follows. If a particular product requires too much labor relative to how much people want it, then it will not be produced. But once the labor time falls to a sufficiently low level by increases in potential productivity, then it will begin to be produced and sold. As productivity continues to increase, the price falls and more workers are employed to bring ever larger quantities of the product to market.
However, once the labor time falls below a certain level, fewer workers are actually required to bring the larger quantity to market, even as production increases. This leads to layoffs in that particular industry after every advance in productivity.
