[60 marks] Suppose that the government wants to introduce a specific tax on a given good. There are two possible goods that can be taxed, X and Y. The government can only tax one good. The objective of the government is to obtain tax revenues but also not to harm consumers too much (since they are voters). The government is asking you to provide an economic analysis that explains how the government should choose which good is better to tax.
Since people in the government are very busy and do not have much time to read you should keep your economic explanation short, no more than two pages. (This is the maximum space you can use, however you will not probably need all of it to properly answer this question)
In your explanation you need to be concise, use the right economic terms and also use graphs (at least two, one for each good) to support your analysis. Graphs are important so you need to make them correctly. There is not a unique right answer. You will be judged on the way you use economic reasoning to arrive at an answer.
Answer both parts of this question
(a) [25 marks] Suppose a consumer has preferences over two goods, x and y, given by the following utility function: . Do the preferences of our consumer satisfy the three main axioms (i.e. assumptions) about preferences? Do the preferences of our consumer satisfy the property of decreasing marginal rate of substitution? Use a graph to illustrate your answer.
(b) [15 marks] Suppose a consumer has preferences over two goods, x and y, given by the following utility function: . Assume that , so the two goods have the same price. Without doing any calculation explain intuitively what should be an optimal consumption choice of the consumer (i.e. how much of each good the consumer should consume). Use a graph to illustrate your answer.