Problem 1: Perfect substitutes, perfect complements As seen in lecture (and in Summary 10), when the two goods are perfect substitutes or perfect complements, one may use a graphical approach to solve the utility maximization problem. Consider the consumer problem: x120 max U(x1, x2) subject to pixi + p2x2 s Y x220 where x, and x2 denote the quantities of good 1 and good 2, p, = 1 and p2 = 2 their respective prices, and Y = 8 is the consumer's income. The consumer preferences are represented by the utility function U. Suppose first that U(x1, X2) = x1 + 3x2 represents the consumer's preferences. 1. What is the shape of the indifference curves? Represent a few of them on an (x1, x2) graph with x2 on the vertical axis. Please draw to scale. 2. Represent the budget line. Label its intersections with the axes and indicate its slope. 3. What is the solution to the consumer problem in this case? Explain and show the solution on your graph. Now assume instead that V(x1, X2) = min(x1, 7) represents the consumer's preferences. 4. What is the shape of the indifference curves? Represent a few of them on an (x1, x2) graph with x2 on the vertical axis. Please draw to scale. 5. Represent the budget line. Label its intersections with the axes and indicate its slope. 6. What is the solution to the consumer problem in this case? Explain and show the solution on your graph