Condition for Convexity in Quasi-Linear Preferences
Indifference curves derived from a quasi-linear utility function are convex if they exhibit a diminishing Marginal Rate of Substitution (MRS), which means they become flatter as one moves to the right along the curve. Since the MRS for such preferences is given by the formula , the condition for convexity is that must be a decreasing function of . In other words, as the quantity of good increases, the value of the first derivative of its utility component, , must fall.
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Step 1: Set up the indifference curve equation: ln(t) + c = u₀ Step 2: Isolate 't' as a function of 'c': t = e^(u₀ - c) Step 3: Differentiate with respect to 'c' to find the slope: dt/dc = -e^(u₀ - c) Step 4: Conclude that the MRS is equal to the result from Step 3.
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Inferring Utility Function Structure from Behavior
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Condition for Convexity in Quasi-Linear Preferences
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