Elasticity of Substitution
Recently, while studying production functions, I revisited a simple yet remarkably insightful concept. I would like to briefly summarize it here. 1. Marginal Rate of Technical Substitution (MRTS) Before diving into the concept of elasticity of substitution, it would be helpful to first review the marginal rate of technical substitution. The Marginal Rate of Technical Substitution (MRTS) measures the rate at which a firm can substitute capital for labor while keeping output constant. It is defined as the slope of an isoquant: $$ MRTS_{LK} = -\frac{dK}{dL}\bigg|_{Q} = \frac{MP_L}{MP_K} $$ Under the cost-minimization condition, the MRTS equals the ratio of input prices: \( MRTS = \frac{w}{r} \), where \( w \) is the wage rate (price of labor) and \( r \) is the rental rate of capital. 2. Elasticity of Substitution The elasticity of substitution measures how easily one input can be substituted for another while ma...