e360_apape_ProfitMaxNotes - and the derivative, which is...

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e360_apape_ProfitMaxNotes.txt 2008-10-28 - 1/1 - Profit Max review, e360, prof: Andreas Pape; date: Tue Oct 28 13:21:48 EDT 2008 * firms choose the quantity q to produce in order to maximize profits * maximizing profits means that, on the last q they make, which we call q*, MR(q*) = MC(q*) * MC is marginal cost, and is the derivative of the Total Cost function with respect to q. * MR is marginal revenue, and is the derivative of the revenue function with respect to q. * Total cost is wL + rK. * Revenue is q * p. * If the firm is a price taker, which is the standard case, p is constant. (There is a fixed external price.) Therefore, d[Revenue]/dq = p. So price takers maximize profits by setting p = MC(q*) * If the firm is not a price taker, then price is determined by a downward-sloping demand curve: p_D(q) for example, p_D(q) = 100 - 10q Therefore, the revenue function is q * p_D(q)
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Unformatted text preview: and the derivative, which is MR(q), is q * p'_D(q) + p_D(q) Note that p'_D(q) is negative, which means that MR(q) < p_D(q); i.e. MR is less than Demand. In our example, where p_D(q) = 100 - 10q, d[ p_D(q) ]/dq = -10. Hence, MR(q) in this example is MR(q) = q * p' + p_D = q * (-10) + (100 - 10q) = -10q + 100 - 10q MR(q) = 100 - 20q Note that MR(q) = 100 - 20q, and p_D(q) = 100 - 10q, so, indeed, MR(q) < p_D(q) * The shutdown footnote on profit maximization: If you are getting NEGATIVE profits, do you have enough REVENUE to cover TOTAL VARIABLE COSTS? If so: sell at q* where MR = MC If not: sell q = 0, and simply pay your FC Note: REVENUE > TOTAL VARIABLE COSTS is algebraically equivalent to PRICE > AVERAGE VARIABLE COSTS if the firm in question is a price taker....
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