1. Assume that an individual has a utility function of U = (wL)^1/2 L where w is the wage rate, and L is the amount of time that they spend working. The individual receives a benefit from consumption, but they also have a distaste for working, which is reflected in the last term. For simplicity, assume that w = 1. a) Calculate this persons optimal labour supply L (5 points). b) Find this persons utility when they work the optimal amount L (5 points). c) Assume that their is a 50% flat tax on income. Calculate this persons optimal labour supply L t with this tax in place. Assume that the tax revenues are not spent on anything that benefits this person. They receive no cash transfer or in kind benefits. (5 points) d) Does this individual work more or less with the tax in place than they did without the tax (from your answer in a)). Explain. (5 points) e) Find this persons utility with the tax in place (5 points). f) Are they better or worse off with the tax in place than without the tax? Explain the intuition. (5 points) g) Assume that there is no longer a tax, but this individual receives a UBI payment of 1 8 from the government. Calculate this persons optimal labour supply L UBI with this tax in place. (5 points) 1 h) Does this individual work more or less with the UBI in place than they did without a UBI (from your answer in a)). Explain. (5 points) i) Find this persons utility with the UBI in place. (5 points) j) Are they better or worse off with the UBI? Explain the intuition. (5 points)