1. Suppose a consumer has an income of 10, and we have π = p^2 = 1. Further, this consumer has standard preferences (decreasing MRS), and chooses x = x^2 = 5 on the resulting budget line.
a) Show this utility-maximizing choice on a graph of the budget set with an indifference curve. Now suppose that the government imposes a tax of $1.00 per unit of x. The consumer chooses point (1, 3), (2, 4) on the resulting budget line. Show this outcome on your graph, including an indifference curve through the new point.