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Marginal Rate of Technical Substitution (MRTS) Calculator

The rate at which a firm can substitute capital for labor while keeping output constant.

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Marginal Rate of Technical Substitution

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Overview

The Marginal Rate of Technical Substitution (MRTS) measures the rate at which a producer can decrease one input, such as capital, and increase another, such as labor, while keeping the total output constant. It is mathematically defined as the ratio of the marginal products of the inputs and represents the slope of an isoquant curve.

Symbols

Variables

MRTS = Marginal Rate of Technical Substitution, MPL = Marginal Product of Labor, MPK = Marginal Product of Capital

MRTS
Marginal Rate of Technical Substitution
Variable
MPL
Marginal Product of Labor
Variable
MPK
Marginal Product of Capital
Variable

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When To Use

When to use: This equation is applied in microeconomic theory to find the optimal combination of production inputs under a fixed budget. It assumes that inputs are substitutable to some degree and is typically used when analyzing firms operating with convex isoquants and diminishing marginal returns.

Why it matters: It allows firms to minimize production costs by ensuring the ratio of marginal physical products equals the ratio of input prices. Understanding MRTS is essential for predicting how firms will respond to changes in the cost of labor relative to the cost of machinery.

Avoid these traps

Common Mistakes

  • Inverting the ratio (calculating MPK/MPL instead of MPL/MPK).
  • Confusing MRTS with the Marginal Rate of Substitution (MRS), which applies to consumer utility rather than production.

One free problem

Practice Problem

A textile factory determines that adding one additional worker increases production by 12 units (MPL), while adding one additional machine increases production by 4 units (MPK). Calculate the Marginal Rate of Technical Substitution (MRTS).

Marginal Product of Labor12
Marginal Product of Capital4

Solve for: mrts

Hint: The MRTS is found by dividing the marginal product of labor by the marginal product of capital.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Pindyck, R. S., Rubinfeld, D. L., & Mehta, P. (2018). Microeconomics (9th ed.). Pearson.
  2. Varian, H. R. (2014). Intermediate Microeconomics: A Modern Approach (9th ed.). W. W. Norton & Company.
  3. Wikipedia: Marginal rate of technical substitution
  4. Pindyck, R. S., Rubinfeld, D. L. (2018). Microeconomics (9th ed.). Pearson.
  5. Pindyck, Rubinfeld, and Mehta, Microeconomics