key term - Long-Run Expansion Path

Definition

The long-run expansion path is a graphical representation of the combinations of inputs that a firm will use to produce different levels of output in the long run, where all inputs can be varied. It shows the firm's optimal input choices as output changes, given the firm's production technology and input prices.

5 Must Know Facts For Your Next Test

1. The long-run expansion path shows the firm's optimal input choices as output changes, given the firm's production technology and input prices.
2. The long-run expansion path is derived by finding the cost-minimizing input combination for each level of output, which occurs where the isoquant is tangent to the isocost line.
3. The slope of the long-run expansion path is equal to the MRTS between the two inputs, which reflects the firm's optimal tradeoff between the inputs.
4. As output increases, the firm will move along the long-run expansion path, substituting between inputs to minimize costs.
5. The long-run expansion path is an important concept for understanding a firm's production decisions and cost structure in the long run.

Review Questions

• Explain how the long-run expansion path is derived and what it represents.
  • The long-run expansion path is derived by finding the cost-minimizing input combination for each level of output. This occurs where the isoquant, which represents the firm's production technology, is tangent to the isocost line, which represents the firm's budget constraint. The long-run expansion path shows the optimal combinations of inputs the firm will use to produce different levels of output in the long run, when all inputs can be varied. It represents the firm's optimal tradeoffs between inputs as output changes, given the firm's production technology and input prices.
• Describe how the slope of the long-run expansion path is related to the Marginal Rate of Technical Substitution (MRTS).
  • The slope of the long-run expansion path is equal to the Marginal Rate of Technical Substitution (MRTS) between the two inputs. The MRTS represents the rate at which one input can be substituted for another input without changing the level of output, and it is equal to the slope of the isoquant. As the firm moves along the long-run expansion path, substituting between inputs to minimize costs, the slope of the path reflects the firm's optimal tradeoff between the inputs, which is determined by the MRTS.
• Analyze how the long-run expansion path can be used to understand a firm's production decisions and cost structure in the long run.
  • The long-run expansion path is a crucial concept for understanding a firm's production decisions and cost structure in the long run. By showing the firm's optimal input choices as output changes, the long-run expansion path reveals how the firm will substitute between inputs to minimize costs. This information can be used to predict how the firm's costs will change as output increases, as the firm will move along the path and adjust its input mix accordingly. Additionally, the long-run expansion path can provide insights into the firm's production technology and the tradeoffs it faces between different inputs, which are essential for understanding the firm's long-run cost structure and decision-making.

Related terms

Long-Run Cost Curve: The long-run cost curve shows the minimum cost of producing each level of output when the firm can adjust all of its inputs, including capital. It is the envelope of the firm's short-run cost curves.

Isoquant:

An isoquant is a curve that shows all the combinations of inputs that produce the same level of output. It represents the production technology available to the firm.

Marginal Rate of Technical Substitution (MRTS): The MRTS is the rate at which one input can be substituted for another input without changing the level of output. It is the slope of the isoquant.