Suppose the utility function of a standard consumer in this economy is as follows:u(x1, x2) = x1 + 5 ln(x2).6

Economists are sometimes interested in the question "what does it mean to be poor?How do we define poverty?" As a first answer, you can say "a person is poor if theirincome is not enough to guarantee a minimum level of utility, say, u".Suppose that in this economy the price of goods 1 and 2 are 1 (that is, p1 = p2 = 1)and that the minimum level of utility needed to clear the poverty line is 100 (that is, u = 100)Of course, we can't define legal poverty in our government statistics based on utility numbers, so we convert these utility values into dollar amounts. Sometimes the government also publishes a "basic consumption bundle" which is the bundle of goods that allows consumers to reach the target utility at the given prices (in this example, it is the bundle of goods that allows you to reach utility 100 at prices p1 = p2 = 1)Hint: du/dx1 = 1, du/dx2 = 5/x^2

Questions:

Given the data above, what is the minimum wealth a person needs in order to clear the poverty line? in other words, what is the minimum amount of money a consumer must spend in order to achieve utility 100?

What is the basic consumption bundle in this economy? In other words, what is the bundle of goods that reaches utility 100 in the cheapest way?

If the price of a good (say, good 1) increases, should the basic consumption bundle be adjusted? How so? A well-labeled picture accompanied by an explanation is sufficient.

Repeat this question using different utility functions (Cobb Douglass and/or different specifications of the quasi-linear).