Problem 3 Food Support and Taxes: The Gates family is a representative wealthy family of New York. They spend their daily income of $1,200 on food and other goods. The price of one unit of food and the price of one unit of other goods are both equal to $1. 3) Putting food on the xaxis and other goods on the yaxis, draw the Gates' budget constraint. Make sure that you indicate the numerical value of both intercepts. What is the numerical value of the opportunity cost of food in terms of other goods? Write the equation of the Gates' budget line. Suppose that the utility function of the Gates is U (my) 2 say, where :r represents food and y represents other goods. The marginal utilities of a." and y are Ur : y and Uyr : 11:, respectively. b) d) e) Derive the MrRSmly as a function of a: and y. Explain in words what the marginal utility U1. is. Suppose that under these circumstances, the Gates' optimal bundle of food and other goods is 600 units of food and 600 units of other goods. The government introduced a subsidy on food. Suppose that the price of food after the subsidy is p = .8. In a new diagram, illustrate the effect of the subsidy on the Gates' budget line. Include the original budget line in your diagram. Ensure you indicate the numerical value of the intercepts of both budget lines. What is the numerical value of the new opportunity cost of other goods in terms of food? Explain in words the opportunity cost of other goods in terms of food. Find the optimal bundle. How many units of food will the Gates purchase after the subsidy? How much do they spend on other goods? Illustrate your answer in the diagram that you drew in part c). Indicate both the optimal bundle before the subsidy and the optimal bundle after the subsidy. What amount of money does the Gates receive from the government through the subsidy? Indicate on the same diagram you used for part c) the amount of the total subsidy that the Gates receive from the government. Government ofcials realize that the Gates (and other aluent families) are unintended subsidy recipients, so they decide to tax the Gates. One oicial argues that the government should tax the Gates with an income tax because an income tax does not skew the Gates' choice, and therefore, the Gates will \"feel\" as if they were taxed less than with a tax on food of the same amount. He also argues that if the government imposes an income tax on the Gates such that they can afford the bundle they bought before the subsidy, the Gates will be equally well off as they were before the government intervention. f) g) h) i) What is the amount of the income tax that allows the Gates to purchase the same bundle they were purchasing before the subsidy? Illustrate on a new diagram the Gates' original budget line, the Gates' budget line after the subsidy, and the Gates' budget line after the income tax. (Hint: Make sure that the amount of the income tax reected in the Gates' aertazt budget line allows them to purchase the some handle that the Gates were buying before the subsidy.) True or false: The Gates will choose the optimal bundle they purchased before the subsidy because it was their optimal choice and is still affordable. Explain. Do you agree with the oicial's argument that the Gates are equally well off? Explain. If the Gates purchase more than 600 units of food after the subsidy and the tax, will they be better off or worse off compared to the original scenario? Explain. If the Gates purchase fewer than 600 units of food after the subsidy and the tax, will they be better off or worse off compared to the original scenario? Explain