真心求助： Labour supply function's slop when leisure is a normal good

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

还是一道英文微观经济题，真心请教各位前辈，如能给出详细解答过程更好，若嫌麻烦，能给出解答步骤也行

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关键词：function Leisure Labour normal Supply function leisure problem normal supply

劳动力函数递减吧？可以考虑下求导哦