6 Monopoly - Monopoly A firm is a monopoly if no other firm produces the same good or a close substitute for it The monopoly is a price setter Its

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Monopoly
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A firm is a monopoly if no other firm produces the same good or a close substitute for it. The monopoly is a price setter. Its demand curve is the market demand curve (since it’s the only firm serving the entire market).
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So, a monopolist faces a downward sloping market demand curve p = D(y). To sell additional units the monopolist must lower its price. Since all units must sell for the same price, p = average revenue (AR). Total revenue is output times price: TR(y) = yD(y)
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In competition, p = MR and were exogenous, determined by the market. In monopoly, p and MR are endogenous, determined by the firm’s choice of level of output y.
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Since the monopolist must reduce price to sell additional units of output, for any positive output, MR is less than price. Marginal revenue MR(y) is the rate at which total revenue changes with changes in output: MR(y) = dTR(y)/dy
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Since TR(y) = yD(y), using the product rule dTR(y)/dy = D(y) + yD’(y) = price + y[slope of the demand curve] = MR(y) As long as y > 0, y[slope of demand curve (-ve)] will be negative and subtracted from price. Therefore, MR will be < price.
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MR and Price Elasticity
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Linear Demand Curves Assume a linear demand curve p = a - by TR = py, therefore TR(y) = ay - by 2 MR(y) = dTR(y)/dy = a - 2by MR is exactly twice as steep as the demand curve. The demand curve intersects the quantity axis at a/b. The MR curve intersects the quantity axis at a/2b. Let’s graph demand, MR and TR:
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1. When TR function has a positive slope, MR is positive. 2. When the TR function is at its maximum, MR is zero. 3. When TR function has a negative slope, MR is negative.
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Maximizing Profit The profit function is expressed as: π(y) = TR(y) - TC(y) Profit is maximized where dπ/ dy = 0. dπ/ dy = dTR(y)/dy - dTC(y)/dy = 0 MR(y) – MC(y) = 0 MR(y) = MC(y) Profit is maximized where MR(y) = MC(y)
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Maximize profit by choosing output (y*) where MC intersects MR . From the demand curve, find the price (p*) that corresponds with the profit maximizing y.
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Π = y*(p* - ATC(y*)) D ATC*
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If ATC lies above the demand curve completely, there is no level of y at which the monopolist can cover its costs. The monopolist will produce 0 (shut down).
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Notice that MC and MR intersect at a point where MR > 0. Demand is price-elastic. The monopolist would never produce on the inelastic portion of the demand curve, where MR < 0.
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Numerical Example A monopolist faces demand p = 100 – y. Its total cost is TC = y 2 + 900. What level of output y will maximize profits and what is price and total profit?
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π= TR – TC = py – (y 2 + 900) = (100 – y)y - y 2 - 900 = 100y - 2 y 2 – 900 Now, there are 2 ways to do this.
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Method #1 Maximize the profit function π= 100y - 2 y 2 – 900 dπ/dy = 100 – 4y = 0 y = 25 π= 100(25) - 2 (25) 2 – 900 = 350 To get price, sub y = 25 into demand: p = 100 – y = 100 – 25 = 75.
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This note was uploaded on 06/18/2011 for the course ECON 2X03 taught by Professor Jamesbruce during the Fall '10 term at McMaster University.

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6 Monopoly - Monopoly A firm is a monopoly if no other firm produces the same good or a close substitute for it The monopoly is a price setter Its

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