How does the elasticity of substitution differ from the marginal rate of technical substitution?

The elasticity of substitution is a measure of how easily one factor of production can be substituted for another in the production process, while keeping the level of output constant. It is defined as the percentage change in the ratio of the factors of production (such as labor and capital) that is required to produce a constant level of output, given a percentage change in the relative prices of those factors. On the other hand, the marginal rate of technical substitution (MRTS) is the rate at which one input can be substituted for another, while keeping the level of output constant. It is the slope of the isoquant (a curve showing all the combinations of inputs that can produce a particular level of output) at a given point. In simple terms, the elasticity of substitution measures the responsiveness of the production process to changes in factor prices, while the MRTS measures the efficiency of substitution between two inputs at a given level of output. While these two concepts are related, they are not the same thing, and can have different implications for production decisions and resource allocation.