This problem is giving me trouble.

Consider an individual who has preferences over consumption and leisure. The utility function is ln (c) + (1 ) ln (l), and his budget constraint is c = w (1 l) where c is consumption, l is leisure time and w is the wage rate. The total time available for work or leisure is normalized to 1. The marginal utility of leisure is MUl = (1 ) /l and the marginal utility of consumption is MUc = /c.

1. Why should the relation MUc w = MUl hold at an optimum?

2. Show that labor supply is independent of the wage rate, w. Explain.

3. Is this a good model of labor supply in the long-run?