Calculating the Income Effect on Free Time
A consumer's preferences for consumption (c) and free time (t) are represented by the utility function U(c, t) = c * t. The consumer has 24 hours available per day, earns an hourly wage (w), and receives unearned income (I). The budget constraint is therefore c = w(24 - t) + I. Calculate the rate at which the consumer's optimal choice of free time changes as their unearned income changes. In other words, find the partial derivative of the optimal free time function, t*(w, I), with respect to I.
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