Mathematical Representation of Income and Substitution Effects PDF

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In this document, you can see the derivation of income and substitution effects using mathematical formulae....

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Income and Substitution Effects Monday, 18 October, 2021

2:57 PM

3.5.1 OPTIMAL ALLOCATION OF FREE TIME: MRT MEETS MRS

𝑦=𝑓(24−𝑡) Thus Alexei’s problem is to choose t and y to maximize 𝑈 (𝑡, 𝑦)U(t,

y) subject to the

(24−𝑡 )y=f(24−t). This is an example of a constrained optimization problem - Problems in which a decision the values of one or more variables to achieve an objective (such as maximizing profit) s constraint that determines the feasible set (such as the demand curve).

𝑦≤𝑓(24−𝑡)y≤f(24−t) This shows that his choice must lie within the feasible set

𝑈(𝑡, 𝑦 )=𝑈(𝑡, 𝑓(24−𝑡))

Utility is maximised at du/dt=0

= 𝑑𝑦/𝑑𝑡

MRT = MRS...