Unformatted text preview: q increases). Claim: If f exhibits decreasing returns to scale then c exhibits diseconomies of scale. Proof: Consider any q and q such that q > q and let λ ≡ q/q . By decreasing returns to scale, we know that f ( L, K ) < λf ( L/λ, K/λ ). The left side of this inequality is q . Dividing both sides by λ and simplifying, this inequality becomes q < f ( L/λ, K/λ ), which means that input levels L/λ and K/λ are more than enough to produce q . As a result, the minimal cost of producing q is strictly less than ( w L + r K ) λ , which itself is c ( q ) /λ . So we have that c ( q ) < c ( q ) /λ . Using the deﬁnition of λ , this becomes c ( q ) < ( q / q ) c ( q ), which simpliﬁes to c ( q ) /q < c ( q ) / q . This condition means that c exhibits diseconomies of scale (average costs increase as q increases). 1...
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This note was uploaded on 11/30/2011 for the course ECON 311 taught by Professor Zambrano during the Fall '08 term at Cal Poly.
 Fall '08
 ZAMBRANO
 Microeconomics, Economies Of Scale

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