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  • Quasi-linear Preferences

  • Derivation of the MRS for a Quasi-Linear Utility Function

MRS in Quasi-Linear Preferences Depends Only on the Non-Linear Good

A key implication of the quasi-linear utility function, u(x,m)=v(x)+mu(x, m) = v(x) + m, is that the Marginal Rate of Substitution (MRS) between the linear good (income, mm) and the non-linear good (xx) depends exclusively on the quantity of xx. This occurs because the marginal utility of income is 1, causing the MRS to simplify to the marginal utility of good xx, which is v′(x)v'(x). Graphically, this means that for any given quantity of xx, the slope of all indifference curves is identical.

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