How the technical rate of substitution and marginal product are relates and what is their difference?
The technical rate of substitution (TRS) and marginal product are related concepts that are used in the field of economics to analyze the production of goods and services. While they are related, they have different meanings and interpretations.
The technical rate of substitution represents the rate at which one input can be substituted for another while keeping the level of output constant. It measures the trade-off between two inputs and indicates the responsiveness of production to changes in the input mix. The TRS is usually expressed as the ratio of the marginal product of one input to the marginal product of another input. Mathematically, TRS = MP1 / MP2, where MP1 is the marginal product of input 1 and MP2 is the marginal product of input 2.
The marginal product, on the other hand, refers to the additional output that is produced when one additional unit of input is used, while keeping all other inputs constant. It measures the change in output resulting from a change in the quantity of one input. The marginal product can be calculated by taking the derivative of the production function with respect to the input variable.
Although the TRS is closely related to the marginal product, they emphasize different aspects. The TRS provides information about the substitutability of inputs, indicating how efficiently one input can be replaced by another. It helps to determine the optimal input mix and identify cost-saving opportunities. In contrast, the marginal product focuses on the productivity of an individual input and provides insight into the effects of increasing or decreasing the quantity of that input.
In summary, the technical rate of substitution evaluates the trade-off between inputs, whereas the marginal product measures the additional output associated with a change in one input. Both concepts are important in understanding production decisions and efficiency levels in economics. Calculating the TRS and marginal product requires analyzing the production function and understanding the relationships between inputs and output.