MRS in Quasi-Linear Preferences Depends Only on the Non-Linear Good
A key implication of the quasi-linear utility function, , is that the Marginal Rate of Substitution (MRS) between the linear good (income, ) and the non-linear good () depends exclusively on the quantity of . This occurs because the marginal utility of income is 1, causing the MRS to simplify to the marginal utility of good , which is . Graphically, this means that for any given quantity of , the slope of all indifference curves is identical.
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MRS in Quasi-Linear Preferences Depends Only on the Non-Linear Good
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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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Figure 5.3b: Constant MRS at a Given Level of Free Time
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