An analyst is attempting to derive the Marginal Rate of Substitution (MRS) for a consumer with the quasi-linear utility function u(t, c) = ln(t) + c, where 't' is free time and 'c' is consumption. Their derivation is shown below:
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.
Identify the fundamental error in the analyst's reasoning.
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MRS in Quasi-Linear Preferences Depends Only on the Non-Linear Good
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An individual's preferences for hours of free time (t) and a composite consumption good (c) are described by the utility function . Calculate this individual's marginal rate of substitution (MRS), defined as the rate at which they are willing to give up units of consumption for an additional hour of free time.
An analyst is attempting to derive the Marginal Rate of Substitution (MRS) for a consumer with the quasi-linear utility function u(t, c) = ln(t) + c, where 't' is free time and 'c' is consumption. Their derivation is shown below:
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.
Identify the fundamental error in the analyst's reasoning.
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