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Does a competitive industry even though levels of output and

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Reference no: EM13339953

Suppose a monopolist produces alkaline batteries that may have various useful lifetimes (X). Suppose also that consumers’ (inverse) demand depends on batteries’ lifetimes and quantity (Q )purchased according to the function

P(Q ,X) = g(X ⋅Q ),

whereg0 <0. That is, consumers care only about the product of quantity times lifetime: They are willing to pay equally for many short-lived batteries or few long-lived ones. Assume also that battery costs are given by

C(Q ,X) = C(X)Q ,

whereC’(X) >0. Show that, in this case, the monopoly will opt for the same level of X as does a competitive industry even though levels of output and prices may differ. Explain your result. Hint: Treat XQ as a composite commodity.

Reference no: EM13339953

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