| 单词 | elasticity of substitution |
| 释义 | elasticity of substitution The ratio of proportional change in relative quantities of two goods demanded to proportional change in their relative prices. Where px and py are the prices of goods X and Y and qx and qy are the quantities, the elasticity of substitution, ES, is defined as - [d(qx /qy)/d(px /py )] [(px /py )/(qx /qy )], to make its sign positive. The better substitutes any two goods are, the higher the ES between them. For perfect substitutes ES is infinite. Where ES > 1, as a good gets relatively cheaper it takes a larger share of total expenditure. If ES < 1, as a good gets relatively cheaper it takes a smaller share of total expenditure. If ES = 1, the two goods take constant shares of expenditure whatever their relative prices. The horizontal axis shows consumption of good X; the vertical axis shows consumption of good Y. (Alternatively, use of factor X and use of factor Y.) The utility function is given by z = [xρ + yρ ]1/ρ. The elasticity of substitution is σ = 1/(1 - ρ). Point E is where x = y = 1, and dy/dx = -1. With perfect substitution, σ → ∞, and the indifference curve is the straight line connecting x = 0, y = 2, and x = 2, y = 0. If the goods are good substitutes, σ > 1. For example, if ρ = 1/2, σ = 2. The indifference curve through E then meets the Y axis at y = 4 and the X axis at x = 4. The case where ρ = 1 corresponds to the Cobb-Douglas case where If the goods are poor substitutes, σ < 1. For example, if ρ = -1, σ = 1/2; the indifference curve through E approaches the asymptote y = 1/2 as x →∞ and the asymptote x = 1/2 as y →∞. If there is no substitutability between X and Y, σ → 0 and the indifference curve is the L-shaped curve DEF. |
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