# Let5 - MR is correct by analyzing its components. MR = (100...

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Let's generalize. Assume that a monopolistic firm faces a linear, downward- sloping market demand curve, described as follows: Q = 100 - P Let's further assume its marginal cost curve is constant at a value of 10. MC = 10 Our firm naturally wants to maximize profits and will therefore aim to satisfy the profit maximizing condition, MC = MR . Marginal costs are constant at ten, so half of our equation is easy. To find our marginal revenue, we first look at the total revenue. Total revenue is simply: R = P * Q Because the monopolist faces the entire market demand curve, price and quantity have a one-to-one relationship. That is, P = 100 - Q . We can rewrite our total revenue as: R = (100 - Q) * Q = 100 * Q - Q^2 The marginal revenue is simply the first derivative of the total revenue with respect to Q . MR = 100 - 2 * Q If you don't feel comfortable with derivatives, you can convince yourself this
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Unformatted text preview: MR is correct by analyzing its components. MR = (100 - Q) - Q (100 - Q ) is the price according to our market demand curve. This 100 - Q represents the marginal revenue brought in by selling the next unit. However, in order to sell the next unit, we had to lower the price by 1 for all units sold (the demand curve has a slope of -1, so the tradeoff between Q and P is 1 for 1). Therefore, on the margin, we lost 1 unit of revenue for all Q units sold. The marginal revenue is then (100 - Q ) - Q = 100 - 2* Q . To solve for the monopolistic equilibrium, we find the quantity at which MR = MC . Solving: 100 - 2 * Q = 10 => Q = 45 At this quantity, the market price would be 100 - 45 = 55 . Assuming no fixed costs, the profits for this firm would be 45*(55 - 10) = 2025 . Naturally, this is a vast improvement for the firm over the competitive outcome of zero profits....
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## This note was uploaded on 12/13/2011 for the course ECO 1320 taught by Professor Staff during the Fall '11 term at Texas State.

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