Abstract
This study derives conditions for existence of a positive sustainable consumption in an economy with an essential exhaustible resource. It does so by approximating technology with a variable elasticity of substitution production function, instead of the constant elasticity of substitution specification widely assumed in previous studies. This approach permits examination of the robustness of results previously derived in the literature to key technological assumptions. It also generates new insights regarding the role of substitutability and technical progress on existence. We find that a capital-resource elasticity of substitution greater than one is sufficient for existence even when the resource is strictly essential; a situation precluded by constant elasticity of substitution specifications. Under an elasticity of substitution lower than one, existence can still be attained (in contrast to the constant elasticity of substitution case) but only through capital-augmenting technical progress. Hicks-neutral technical progress is neither necessary nor sufficient for existence. A sufficiently high resource-augmenting technical progress thwarts existence of a positive sustainable consumption.
Highlights
This paper examines the role of input substitutability and technical progress on the existence of positive sustainable consumption in an economy with an essential exhaustible resource
Low substitutability and limited resource productivity are confounded. Under these technological assumptions studies found that σ kr < 1 is sufficient for inexistence of a positive sustainable consumption
We develop a framework capable of 1) linking capital-resource substitutability with the existence of positive sustainable consumption when the resource is strictly essential regardless of the value of σ kr, 2) linking biased technical progress with existence, and 3) capturing compensations between σ kr and technical progress that result in existence of a positive sustainable consumption
Summary
This paper examines the role of input substitutability and technical progress on the existence of positive sustainable consumption in an economy with an essential exhaustible resource. Low substitutability and limited resource productivity are confounded Under these technological assumptions studies found that σ kr < 1 is sufficient for inexistence of a positive sustainable consumption. It remains unclear whether limited substitutability (i.e. σ kr < 1 ) is still sufficient for inexistence when average product of the resource is unbounded?. By approximating technology with a transcendental specification, our analysis: 1) nests many results in previous studies, 2) examines the robustness of others, and 3) generates new insights regarding the role of substitutability and technical progress on existence of positive sustainable consumption
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