### Marginal Rate of Technical Substitution

Marginal rate of technical substitution (MRTS) may be defined as the rate at which the producer is willing to substitute one factor input for the other without changing the level of production.

In other words, MRTS can be understood as the indicator of rate at which one factor input (labor) can be substituted for the other input (capital) in the production process while keeping the level of output unchanged or constant.

If we denote labor by ‘L’ and capital by ‘K’, then MRTS of labor for capital can be expressed as

**Table 1: marginal rate of technical substitution (MRTS)**

Combination | Capital (C) | Labor (L) | MRTS_{L,K} |
Output |

A | 12 | 1 | 100 | |

B | 8 | 2 | 4:1 | 100 |

C | 5 | 3 | 3:1 | 100 |

D | 3 | 4 | 2:1 | 100 |

E | 2 | 5 | 1:1 | 100 |

In the above table, there are five different combinations of labor and capital, all of which yield the same level of output.

We can see in combination A that 12 units of capital and 1 unit of labor have jointly produced 100 units of output. When the producer moves to combination B, he gave up 4 units of capital in order to add 1 unit of labor input while keeping the production level unchanged. Hence, MRTS of labor for capital is 4 in this case.

Likewise, if we compare the combinations B and C, the consumer gave up 3 input units of capital in order to add 1 unit of labor. Therefore, MRTS in this case is 3.

In the same way, the MRTS is 2 and 1 between the combinations C and D, and D and E, respectively.

### Principle of Marginal Rate of Technical Substitution

Marginal rate of technical substitution is based on the principle that the rate by which a producer substitutes input of a factor for another decreases more and more with every successive substitution.

If we assume labor (L) and capital (K) to be the two inputs of a production process, the principle of MRTS states that the value of MRTS_{L,K} decreases with subsequent substitution of labor for capital. And, this diminishing rate of MRTS is also apparent from the table 1 given above.

Initially, when the producer moved from combination A to combination B, the rate of MRTS was calculated to be 4. When the producer moved to combination C, the rate of MRTS fell and became 3. In the same way, with each successive addition of constant unit of labor, the MRTS were calculated to be 3, then 2 and finally, 1.

Clearly, the marginal rate of technical substitution has diminished more and more as the producer kept on substituting input of labor for capital.

**Figure 1: marginal rate of technical substitution **

### Causes of Diminishing Marginal Rate of Technical Substitution

Marginal rate of technical substitution is diminishing due to following reasons.

#### Imperfect substitutability of the factors

Two factors cannot substitute each other perfectly because they have their own uses in the production process.

Besides, if the factors could perfectly substitute each other, increase or decrease in either of the factors won’t bring any changes in the marginal rate of technical substitution.

#### Inadequacy of the factor

Substituting one factor for the other continuously causes scarcity of the factor being replaced. As a result, the factor being tradeoff won’t be able to make as much contribution as it should have for the efficient production.

Therefore, although the producer had sacrificed more units of capital input in the beginning, the rate of substitution fell with additional substitutions.