Assume that an individual works to generate her income Y. Work involves exerting effort, and that is costly for the individual we are studying. Suppose that the individual can choose an effort level, which we denote by e, where e is any number between zero and ten. The income of the individual is a function of her effort level and follows the following formula: Y(e) = 5 + 10e. As we said above, exerting effort is costly for the individual and as a result, her total utility after having exerted effort at level e is given by: U(e) = Y (e) 2 e 2 Where is the utility cost of exerting a level of effort e.

Suppose now that the government imposes an income tax. The income tax rate, t, is a number between zero and one and it implies that any individual with an income Y (e) pays t Y (e) to the government.

Suppose the individual is choosing her effort level e to maximise her utility. Assuming that there is an income tax t, which effort level would she choose? What would be her income after exerting effort?