bart11 said:Calculate the elasticity of substitution between y and x for F(x,y) = 10x^2 + 15y^2
I was able to calculate the Marginal Rate of Substitution as 20x/30y but I'm not sure how to proceed past that. The answer in the book is -1. Any and all help appreciated!
dwsmith said:denote rho as the power.
Then elasticity of substitution is
$\dfrac{1}{1-\rho}$
If the power is different, you would have to use the formula.
Elasticity of substitution is a measure of how easily one input (such as labor) can be replaced with another input (such as capital) without changing the overall output. It is used to analyze the production process and determine the optimal combination of inputs to use in order to produce the desired level of output.
Elasticity of substitution can be calculated using the formula: ε = (∂lnK/∂lnL), where K is the quantity of capital and L is the quantity of labor. This formula measures the percentage change in the ratio of capital to labor, as one input is substituted for the other.
A high elasticity of substitution means that the two inputs can be easily substituted for each other, with minimal impact on the overall level of output. This suggests that the production process is flexible and can adapt to changes in input prices or availability.
Elasticity of substitution is important because it helps firms make decisions about how to produce goods and services in the most efficient and cost-effective way. It also has implications for the distribution of income between labor and capital, as well as the overall efficiency of the economy.
The elasticity of substitution can be influenced by factors such as technological advances, the availability and cost of inputs, and the substitutability of inputs in the production process. It can also vary across industries and time periods, depending on the specific economic conditions.