What would it mean if an expansion path eventually had a negative slope? Like the letter U on its' side?


And expansion path that looks like a letter U on its side (like a c or a backwards c?)
Dont know. I think a graph of an expansion path would be time on the x axis, some level of activity on the y axis. (possibly, the x axis could be some level of inputs) Anyway, for any x-value, there would be one and only one y (level) value. A sideways U shape would have two.

That said, however, an expansion path with a negative slope would indicate a period of contraction.

The production engineers at Impact Industries hace dervied the expansion path shown in the following. The prcie of labor is $100 per unit

To understand what a U-shaped expansion path implies, let's first clarify what an expansion path represents.

An expansion path shows the relationship between the outputs produced by a firm as it increases its level of inputs. It maps out the different combinations of inputs that result in different levels of output for a firm. Typically, the expansion path is depicted on a graph with the level of inputs on the x-axis and the level of output on the y-axis.

Now, when we talk about a U-shaped expansion path, it means that as the firm increases its level of inputs, there is initially an increasing level of output. However, after reaching a certain point, further increases in inputs start to decrease the level of output. This results in a downward-sloping portion of the expansion path resembling a U-shape.

The U-shaped expansion path represents a stage of diminishing returns to scale. Initially, as the firm expands its inputs, it experiences increasing returns to scale, where each additional unit of input leads to a greater-than-proportional increase in output. However, beyond a certain input level, the firm starts to experience diminishing returns, where each additional unit of input leads to a lesser-than-proportional increase in output. This results in a negative slope on the expansion path.

To determine the exact reasons behind the U-shaped expansion path and understand the underlying causes, further analysis of the specific industry, technology, or production process would be necessary.