Technical Rate of Substitution (TRS)
Calculate the rate at which one input can be substituted for another while maintaining constant output.
What is the Technical Rate of Substitution?
The Technical Rate of Substitution (TRS), also frequently referred to as the Marginal Rate of Technical Substitution (MRTS), is a fundamental concept in microeconomics and production theory. It measures the rate at which a firm can substitute one factor of production (Input 1, often Labor) for another (Input 2, often Capital) while keeping the total level of output constant.
Geometrically, the TRS represents the absolute value of the slope of an isoquant at any given point. An isoquant is a curve that shows all the possible combinations of inputs that yield the same quantity of output.
The TRS Formula
The Technical Rate of Substitution is calculated using the ratio of the Marginal Products of the two inputs involved. The formula is:
TRS = MP₁ / MP₂
Where:
- MP₁ (Marginal Product of Input 1): The additional output generated by adding one more unit of Input 1 (e.g., Labor).
- MP₂ (Marginal Product of Input 2): The additional output generated by adding one more unit of Input 2 (e.g., Capital).
How to Interpret the Result
The resulting number tells you how many units of Input 2 you can give up if you add one unit of Input 1, without affecting total production.
- If TRS = 4: You can replace 4 units of Capital with 1 unit of Labor, and your output remains exactly the same.
- If TRS = 0.5: One unit of Labor can only replace 0.5 units of Capital. This suggests Labor is less productive relative to Capital at this specific margin.
Economic Significance
Understanding the TRS is crucial for firms aiming to minimize costs. In an efficient market, a cost-minimizing firm will adjust its inputs until the Technical Rate of Substitution equals the ratio of the input prices:
TRS = Price of Input 1 / Price of Input 2
If the TRS is higher than the price ratio, the firm should use more of Input 1 and less of Input 2 to lower costs. If it is lower, they should shift towards using more of Input 2.
Example Calculation
Imagine a furniture factory producing chairs:
- Input 1 (Labor): Adding one worker increases production by 10 chairs per day (MP₁ = 10).
- Input 2 (Machinery): Adding one machine increases production by 5 chairs per day (MP₂ = 5).
Using the calculator above:
TRS = 10 / 5 = 2.0
This means 1 worker is technically equivalent to 2 machines in terms of output at the margin. To maintain the same production level, if the factory hires one more worker, they can reduce their machinery usage by 2 units.