Mathematical Argument for a Pareto Improvement via Infinitesimal Reduction in Output
A mathematical argument demonstrates that a Pareto improvement is possible starting from the profit-maximizing output level () where a negative externality exists. An infinitesimal decrease in production from has no effect on the plantation owner's profit, as price equals marginal private cost at this point. However, this same reduction benefits the fishermen by an amount equal to the marginal external cost (), which is positive. This creates a situation where the fishermen's gain is greater than the plantation's loss (which is zero), opening the door for a mutually beneficial agreement through a compensatory payment. [1]
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Graphical Representation of the Banana Market with Negative Externalities (Figure 10.3)
Confirmation of Profit Maximum at Point A Using the Second-Order Condition
Mathematical Argument for a Pareto Improvement via Infinitesimal Reduction in Output
Cause of Upward-Sloping MPC in Banana Production
A plantation produces bananas for a large, competitive global market, where it can sell as many tons as it wants at a fixed price of $400 per ton. The table below shows the plantation's marginal private costβthe cost to the plantation itself for producing one additional ton of bananasβat various levels of output. Analyze the data to determine the quantity of bananas the plantation should produce to achieve the highest possible profit.
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A banana plantation operates in a competitive market, selling its produce at a constant world price of $400 per ton. The plantation's managers have determined that their profit is highest when they produce 80,000 tons per year. At this specific output level, the cost to the plantation to produce one additional ton of bananas is also $400. Given that producing even more bananas requires more intensive use of the land and thus increases the cost per additional ton, what would be the immediate effect on the plantation's total profit if it decided to increase its output to 80,001 tons?
A chemical company operates in a perfectly competitive market and sells its product at a constant price of $150 per barrel. The company's internal cost to produce each additional barrel rises as output increases. This production process also generates waste, which imposes a clean-up cost on the local community, a cost the company does not pay. To maximize its own profits, the company should increase its production until its internal cost to produce the very last barrel is:
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A banana plantation operates in a competitive market where the price for bananas is fixed at $400 per ton. The plantation is currently producing 70,000 tons per year, and at this level of production, the cost to produce one additional ton of bananas is $350. To maximize its profit, the plantation should decrease its production.
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A banana plantation operates in a competitive market, selling its entire output at a stable price of $400 per ton. The plantation is currently producing 80,000 tons, at which point the marginal cost (the cost of producing one additional ton) is also $400. A consultant reviews the operations and recommends reducing production to 60,000 tons, where the marginal cost is only $325 per ton. The consultant argues, "By producing at a level where the cost of the last ton is well below the selling price, the plantation will increase its overall profit." Which of the following statements best evaluates the consultant's recommendation?
A company manufactures high-performance bicycle frames. Due to the specialized labor and materials required, the cost of producing each additional frame increases as production ramps up. The company sells these frames in a competitive global market. Currently, the market price is $700 per frame, and the company is producing 500 frames per month, which is its profit-maximizing output level. A new trade agreement is signed, causing the global market price for these frames to permanently increase to $750. To adapt and continue to maximize its profits, what action should the company take regarding its monthly production level?
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Description of Figure 10.2: The Plantations' Profit-Maximizing Output and External Costs
Learn After
A factory operates in a competitive market and produces at the quantity where its marginal private cost equals the market price, maximizing its own profit. This production process, however, pollutes a river, imposing a cost on a downstream fishery. If the factory were to reduce its output by a single, infinitesimally small unit from this profit-maximizing level, what would be the immediate effect on the profits of the factory and the fishery?
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Consider a profit-maximizing firm operating in a competitive market, whose production process generates a negative externality. A statement is made: 'An infinitesimally small, mandated reduction in output from the firm's current level will necessarily lead to a situation where the monetary gain to those harmed by the externality is greater than the monetary loss to the firm.' Is this statement true or false?
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A competitive firm's profit is maximized at the output level where the market price equals its marginal private cost. Consequently, for an infinitesimally small reduction in output starting from this profit-maximizing point, the change in the firm's profit is effectively ________.
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A firm's production process generates a negative externality affecting a third party. The firm is currently producing at its private profit-maximizing output level. An economist argues that a small reduction in output from this point can create a net social gain. Arrange the following statements to reconstruct the logical flow of this argument.
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