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11th lecture - Economics 101 Lecture 11 Example 11.1 How...

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Economics 101 Lecture 11
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Example 11.1. How should Leroy divide his time between… …picking apples… …and writing pulp fiction?
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A men's magazine will pay Leroy 10 cents per word to write fiction articles. He must decide how to divide his time between writing fiction, which he can do at a constant rate of 200 words per hour, and harvesting apples from the trees growing on his land, a task only he can perform. His return from harvesting apples depends on both the price of apples and the quantity of them he harvests.
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Earnings aside, Leroy is indifferent between the two tasks. The amount of apples he can harvest depends on the number of hours he devotes to this activity: Hours Total bushels Additional bushels 8 1 8 4 2 12 3 3 15 2 4 17 1 5 18
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For each hour Leroy spends picking apples, he loses the $20 he could have earned writing pulp fiction. He should thus spend an additional hour picking as long as he will add at least $20 worth of apples to his total harvest.
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For example, if apples sell for $2.50 per bushel, Leroy would earn $20 for the first hour he spent picking apples, but would earn only an additional $10 if he spent a second hour. Hours Total bushels Additional bushels 8 1 8 4 2 12 3 3 15 2 4 17 1 5 18
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Thus, at a price of $2.50 per bushel, Leroy would allocate 1 hour to picking apples, during which time he will harvest 8 bushels. Hours Total bushels Additional bushels 8 1 8 4 2 12 3 3 15 2 4 17 1 5 18
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If the price of apples then rose to $5 per bushel, it would pay Leroy to devote a second hour to picking, which would mean a total of 12 bushels of apples. Hours Total bushels Additional bushels 8 1 8 4 2 12 3 3 15 2 4 17 1 5 18
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Once the price of apples reached $6.67 per bushel, he would devote a third hour to picking apples, for a total of 15 bushels. Hours Total bushels Additional bushels 8 1 8 4 2 12 3 3 15 2 4 17 1 5 18
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If the price rose to $10 per bushel, he would pick for four hours and get 17 bushels. Hours Total bushels Additional bushels 8 1 8 4 2 12 3 3 15 2 4 17 1 5 18
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And, finally, once the price of apples reached $20 per bushel, Leroy would supply five hours of apple- picking services, and would harvest 18 bushels of apples.
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