Analyzing a Calculation Error for the Marginal Rate of Substitution
An economics student is analyzing a consumer's preferences for coffee (C, on the horizontal axis) and tea (T, on the vertical axis), given by the utility function U(C, T) = 2C + ln(T). The student calculates the marginal rate of substitution (MRS) as follows:
- Marginal Utility of Coffee (MUc) = ∂U/∂C = 2
- Marginal Utility of Tea (MUt) = ∂U/∂T = 1/T
- MRS = MUt / MUc = (1/T) / 2 = 1/(2T)
Identify the conceptual error in the student's calculation of the MRS. Explain the correct principle and provide the correct final calculation.
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