Im not sure if this is the right place, but I have an optimization problem where I assume we are supposed to use the Lagraingian method: Consider the labour supply problem for an individual over an entire year. Suppose the individuals utility is described by the function U = (C^0.5) x (H^0.5). Further, suppose that the individuals combined time/income constraint is given by the equation C + wh = Tw, where T = 8760 is the number of hours in a standard year. Suppose the initial wage rate is $ 10/hour. Suppose that the government imposes a progressive income tax of 10% on all income above $ 25,000. That is, the individual pays no tax on the first $ 25,000 they earn. However, any income above $ 25,000 per year is taxed at a rate of 10%. Given this tax, what are the individuals optimum choices of consumption (C) and leisure (H). I know how to do the problem without the tax, but i have no idea how to deal with the tax. Any help is greatly appreciated (its gonna be on a final i have tomorow, so the faster the better. Thanks.