Sarah has preferences that satisfy all the regular assumptions over the goods x and X2. She has an income of 80 dollars and faces the prices pr-2 and p2-8 respectively. a) Suppose Sarah's preferences can be represented by the utility function U(x, x) = min [x,x]. What are Sarah's optimal choices of x, and x, at these prices and income? b) Suppose that the price of good 1 increases to 3 dollars. What is Sarah's new consumer optimum? The government would like to compensate Sarah as a result of the higher price. How much income would the government need to give Sarah so that she can just afford her original consumption bundle in a)? Describe why this is a "money-metric" measure of the welfare loss associated with the price change.