In economics, an expansion path, also known as the long-run cost minimization path, shows the optimal combinations of two inputs a firm chooses as it expands its production level. It’s essentially a roadmap for minimizing costs while increasing output. Here are some major types of expansion paths, along with a diagram to visualize them:
1. Linear Expansion Path:
This is the most common type, where the expansion path appears as a straight line from the origin. It occurs when factors are perfectly substitutable, meaning one can fully replace the other without affecting output. In the diagram, each isoquant (green curves) represents a constant output level, while isocost lines (blue lines) represent different total input costs. Tangency points (where lines touch) show the optimal input combination for each output level. As output increases, the firm moves along the expansion path, using more of both inputs proportionally.
2. Curved Expansion Path:
This type arises when factors are imperfectly substitutable. Meaning, increasing one input can only partially compensate for a decrease in the other. This results in a curved expansion path, often S-shaped, as the firm adjusts its input mix gradually. The initial segment might see more emphasis on one factor, transitioning to a balanced use at medium outputs, and then favoring the other factor as output expands further.
3. Zigzag Expansion Path:
This occurs in cases of non-homogenous production functions, where increasing one input might lead to disproportionate increases in output at certain points. This creates a “kinked” expansion path, where the slope changes abruptly due to shifts in marginal rate of technical substitution (MRTS).
4. Expansion Path under Changing Factor Prices:
The expansion path can shift based on the relative prices of input factors. If the price of one factor increases, the isocost lines become flatter, leading the expansion path to favor the cheaper factor. This results in a change in the optimal input mix and a “pivot” in the path’s direction.
Imagine a graph with two axes: X-axis for one input (e.g., Labor) and Y-axis for the other input (e.g., Capital). Overlaid on this are:
Green curves: Isoquants, representing constant output levels (Q1, Q2, Q3…).
Blue lines: Isocost lines, representing constant total input costs (TC1, TC2, TC3…).
Black line: Expansion path connecting the tangency points of isoquants and isocost lines for each output level.
This basic diagram can be adapted to illustrate the different types of expansion paths mentioned above by adjusting the shapes and slopes of the curves and lines.
Remember, the specific shape and behavior of the expansion path depend on the firm’s production function and factor prices. Analyzing these paths helps businesses make informed decisions about resource allocation and cost optimization during expansion.
2.6 Ridge Line
The term “ridge line” can have different meanings depending on the context. Here are two possible interpretations:
1. Ridge lines in economics:
In production theory, a ridge line is a curve that connects the points of diminishing marginal returns on an isoquant map. An isoquant is a curve that shows all the different combinations of two inputs that can produce the same level of output.
Ridge line in economics
The ridge line is significant because it separates the region of production where both inputs are used efficiently from the region where one input is being overused relative to the other. In other words, any point on the ridge line represents the most efficient way to produce a given level of output, given the available technology and input prices.
2. Ridge lines in data visualization:
In data visualization, a ridge line is a type of chart that shows the distribution of a continuous variable for multiple groups of data. It is similar to a stacked histogram, but the data is displayed as smoothed curves instead of bars.
Ridge line in data visualization
Ridge lines can be useful for comparing the distributions of different groups, especially when the groups have overlapping values. They can also be used to identify outliers or trends in the data.