Deriving the Lender's Minimum Share
In a credit market with one lender and three active borrowers, each borrower's project generates a total output normalized to 1. The lender receives an identical share, 's', from each of the three borrowers, while each borrower keeps the remaining portion (1-s) of their own output. To ensure the lender is the highest earner in this arrangement, their total income must be at least as large as any single borrower's income. Formulate the inequality that represents this condition and solve it to determine the minimum value of 's'. Show your steps.
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Introduction to Microeconomics Course
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Ch.9 Lenders and borrowers and differences in wealth - The Economy 2.0 Microeconomics @ CORE Econ
The Economy 2.0 Microeconomics @ CORE Econ
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In a credit market with a single lender and three active borrowers, each borrower's project generates a total output normalized to 1. The lender receives an identical share, 's', from each of the three borrowers, while each borrower keeps the remaining portion (1-s) of their own output. What is the minimum share 's' required for the lender's total income to be at least as large as the income of any single borrower?
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