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Mathematical Derivation Oct 12 - ECON

Mathematical Derivation Oct 12 - ECON - Mathematical...

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Unformatted text preview: Mathematical Derivation for Q* • The monopolist does not have a schedule that relates price to output (i.e, no supply curve); no distinct relationship between Q and P • Mathematical analysis requires calculating MR from the demand schedule, setting MR = MC, and t hen solving for Q*. A. Calculating MR If Q = a – bP then invert to obtain P = a/b – (1/b)Q Now double the slope to obtain MR = a/b – (2/b)Q B. Set MR = MC and solve for Q* • Example: calculate the profit earned by a monopolist who has cost C(Q) = 100+ 2Q2 if market demand is Q = 30 – (1/3)P. Use “rule of thumb” to calculate demand elasticity at optimal price. () ( ( ) ) Plug into Demand to get () – We may plug these two into and solve for E. ...
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