Solutions Calculus

Consider the problem of maximizing u (c, ?) subject to pc + w? = wT +Y, where the c is consumption

Question: Consider the problem of maximizing u (c, ?) subject to pc + w? = wT +Y, where the c is consumption, ? is leisure time, T is the total time endowment, and Y is non-wage income. Prove that the labour supply function is downward sloping only if leisure is a normal good.

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