1. On a faraway planet, Toydarians have utility defined only over blue milk M and moisture vaporators V. Their utility function is defined in the following way: U MV2. The aliens must satisfy the budget constraint of I = PmM+P,V. (a) Using the Lagrange method, solve for optimal amounts of M and V. (b) Suppose that I = 40 wupiupi (the local currency), PM 1, Py = 1. How happy are the Toydarians? (c) Now assume that the government must tax aliens to subsidize the manufacture of a large, moon-shaped space station. If the government taxes each alien 10 wupiupi, how happy are the aliens? (d) Now suppose that the government decides to tax blue milk instead. What amount must the government tax each unit of blue milk to generate the same revenue? What would be the amount of the tax if the government taxed va- porators instead? How happy are the aliens when blue milk is taxed? When vaporators are taxed? (e) Which tax policy would you recommend