Impact of Non-Labor Income on Labor Choice with Quasi-Linear Preferences
An individual's preferences are described as 'quasi-linear' if their utility function can be written in the form U(t, y) = v(t) + y, where 't' is hours of free time and 'y' is consumption of a good. The individual can produce the good according to a production function y = f(h), where 'h' are hours of work and h = 24 - t. Assume the individual also receives a fixed amount of non-labor income, M. Using calculus, analyze why the optimal choice of working hours for this individual is independent of the amount of non-labor income (M) they receive. Show the setup of the optimization problem and explain how the first-order condition leads to this conclusion.
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