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Interpreting the First-Order Condition
In a constrained optimization problem where an individual chooses amounts of two goods, x and y, to maximize a value function v(x, y) subject to a constraint g(x, y) = c, the first-order condition is often expressed as the ratio of the partial derivatives of the value function being equal to the ratio of the partial derivatives of the constraint function. Explain the economic intuition behind this mathematical equality. What does each side of the equation represent in terms of the individual's choice?
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Ch.5 The rules of the game: Who gets what and why - The Economy 2.0 Microeconomics @ CORE Econ
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Interpreting the First-Order Condition