Consider the following two concepts. Are these concepts properly defined?Definition I) A diseconomy of scale is when long run average costs rise as output (q) increases.Definition II) A fixed-proportions production function is one where the marginal rate of technical substitution is constant at all points.

Question

BlackTom AI · Accepted Answer

We start by restating the question in our own words to frame the evaluation: We are asked whether Definition I and Definition II are proper definitions of two economic concepts: (I) diseconomies of scale and (II) fixed-proportions production function. Then we assess each answer choice by evaluating each definition carefully.

Option a: 'a. Definition II is correct but definition I is incorrect.' For Definition II, claiming that a fixed-proportions production function has a constant MRTS at all points is suspicious. In a fixed-proportions (Leontief) production function, inputs must be used in fixed proportions; you cannot substitute one input for another, so the MRTS is not well-defined as a positive, finite, constant rate across all points. In many regions, MRTS is either infinite or zero depending on which input is binding, and at interior points there is effectively no smooth MRTS. Therefore, Definition II is not correctly describing the fixed-proportions case. Since Definition I is actually correct, this option incorrectly asserts II is correct, making this option unlikely.

Option b: 'b. Definition I is correct but definition II is incorrect.' Definition I states that a diseconomy of scale occurs when long-run average costs rise as output increases. This is the standard characterization of diseconomies of scale: as scale expands, average cost eventually climbs. This is correct by textbook definition. Definition II claims a fixed-proportions production function has a constant MRTS at all points. As discussed, a Leontief/fixed-proportions technology does not allow substitution between inputs, so MRTS is not constant across all points; it is not a well-behaved constant slope everywhere. Thus II is incorrect. Therefore, this option aligns with the accurate assessment of both definitions.

Option c: 'c. Both terms are correctly defined.' This would require Definition II to be a correct description of a fixed-proportions production function with a constant MRTS at all points. As explained, the MRTS for a fixed-proportions technology is not constant across all points (and often undefined in the usual smooth, differentiable sense). Hence this option is false.

Option d: 'd. Both terms are incorrectly defined.' Given that Definition I accurately describes diseconomies of scale, this option mislabels I as incorrect. Since I is a standard correct statement, this option is also incorrect.

In summary, option b correctly identifies I as correct and II as incorrect, while the other options either misstate II or incorrectly judge the definitions of I or both. The distinctions hinge on the standard understanding of diseconomies of scale versus the substitution properties of a fixed-proportions production function, where MRTS is not constant across all input combinations.

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