Explanation Given information: A cost function C ( x ) gives the total cost of producing x units of a product. The elasticity of the cost at quantity x , E c ( x ) is defined to be the ratio of the relative rate of change of cost divided by the relative rate of change of quantity. Formula used: The elasticity of demand E ( p ) at price p for the demand function q = f ( p ) is defined to be E ( p ) = − p f ' ( p ) f ( p ) . Proof: A cost function C ( x ) gives the total cost of producing x units of a product. A relative rate of change of cost with respect to x is, d d x ( C ( x ) ) C ( x ) = C ' ( x )

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Chapter 5.3, Problem 25E

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Toprove: Ec(x)=x⋅C'(x)/C(x), where C(x) is the cost function which gives the total cost of producing x units of a product, and the Ec(x) is the elasticity of cost at quantity x.

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Chapter 5.3, Problem 24E

Chapter 5.3, Problem 26E

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Toprove: E c ( x ) = x ⋅ C ' ( x ) / C ( x ) , where C ( x ) is the cost function which gives the total cost of producing x units of a product, and the E c ( x ) is the elasticity of cost at quantity x .

Solution Summary: The author explains how the cost function C(x) gives the total cost of producing x units of a product.

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Toprove: Ec(x)=x⋅C'(x)/C(x), where C(x) is the cost function which gives the total cost of producing x units of a product, and the Ec(x) is the elasticity of cost at quantity x.

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