The Marginal Rate of Technical Substitution (MRTS) quantifies the rate at which one input in the production process can be substituted for another while maintaining the same level of output. It reflects the trade-off between inputs, such as labor and capital, in the production function.
The MRTS is derived from the slope of an isoquant, a curve showing all input combinations producing a given output. Mathematically, the MRTS is expressed as the negative ratio of the marginal product of one input over the marginal product of another input. Specifically, if we consider labor (L) and capital (K) as the two inputs, the MRTS of labor for capital is given by:
Here, ΔK and ΔL represent small changes in capital and labor, respectively, and MPL and MPK are the marginal products of labor and capital, respectively. The negative sign indicates that an increase in one input compensates for a decrease in the other when maintaining a level of output.
This concept is essential for firms to optimize their input mix, especially when input prices change, ensuring cost-efficient production while maintaining output levels.
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