Suppose Hillary has preferences represented by U(x,y)=2xy​. Her income is $40, the price of good x is $4, and the price of good y is $2. In this question, let's evaluate policies that government may implement to encourage the consumption of x. a. Imagine the government offers a per unit subsidy for x. Specifically, for every unit of x, she receives $2. Find the optimal bundle . b. Imagine instead that the government simply gives Hillary a lump sum of $40 to be spent however she wants. Find the optimal bundle . c. Which bundle does Hillary prefer? Illustrate both bundles on the graph containing clearly labelled budget constraints and indifference curves . d. Would the government want to unequivocally implement either policy a or b ? If it depends, briefly discuss. Hint: to implement the policy, the government also needs to think about the implementation cost .