MHB Calculating elasticity of substitution help

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To calculate the elasticity of substitution between goods x and y for the function F(x,y) = 10x^2 + 15y^2, the Marginal Rate of Substitution (MRS) has been determined as 20x/30y. The elasticity of substitution can be expressed using the formula 1/(1-ρ), where ρ represents the power in the utility function. Clarification is needed on the value of ρ, as the book's answer of -1 suggests a specific interpretation of the function. The discussion highlights confusion regarding the application of the formula and the concept of ρ in calculating elasticity. Understanding these concepts is essential for accurately determining the elasticity of substitution.
bart11
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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!
 
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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!

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.
 
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.

Sorry but I'm not sure if I follow. Rho? And I believe the book taught us using the formula so I may be a little confused. Thanks for the help!
 

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