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4

The profit of a firm $i$ is given by: $$ \pi_i(p) = p q_i - C_i(q_i) $$ where $p$ is the price, $q$_i is the output of firm $i$ and $C_i(.)$ is the cost function which differs across firms. The first order condition gives: $$ p = \frac{\partial C_i(q_i)}{\partial q_i} = MC_i(q_i^\ast) $$ This shows how to obtain the optimal supply of firm $i$, i.e. where $MC(...


2

Premise of your question is simply false. You state (emphasis mine): Price elasticity of demand $\mathrm{e_{D,P} = \dfrac{dD}{dP}. \dfrac{P}{Q^*}}$ clearly depends on the levels of price and quantity. Incorrect. Consider trivial counter example. A perfectly reasonable demand can be given by: $$ Q = A p^{-\epsilon} $$ where $Q$ is quantity, $p$ price and $...


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