SOLUTIONS TO 100A, QUIZ 1

  1. Say that the price of y is initially 1 and so the price of x is initially 2. Then the budget was 24. Now it is 48 and the price of y doubles to 2. If she still buys 2 units of y, this costs 4, leaving only 44 to buy x, so 22 units of x is the most she can afford. a)
  1. Look at the budget equations. In year 1, 4x + y = 40, so y = 40 – 4x. This line has a slope of –4, a y-intercept of 40 and an x-intercept of 10. In year 2, 21x + 5y = 40, so 5y = 40 – 21 x, so y = 8 – 4.2x. The slope of this line is –4.2, so it is steeper than the old one. It has a y-intercept of 8 and an x-intercept less than 2. Thus, the line segment in the positive quadrant is completely below the old one and is steeper than it. c)
  1. He needs another 100 to buy the 100 units of x, and he needs another 250 to buy the 50 units of y, so he needs an additional 350 to buy his original bundle. b)
  1. His income is 378 + 42G. With it, he can buy 6V. So 378 + 42G = 6V, so 6V - 42G = 378. c)
  1. The bundle (28,43) is the same for him as the bundle (16,31). This bundle is equivalent to (24,23), as they are perfect substitutes in this range. b)
  1. Flawed question.
  1. Monotonic (or more properly, positively monotonic) means that more is always preferred to less. c)
  1. |c-2| + |7-m| = |2-5| + |7-4| = 3 + 3 = 6 for the point (5,4). For the point (8,1), the sum of the deviations is 12. For the points (2,1), (8,7), and (5, 10), the sum is 6. For the point (2,7), the sum is 0. For the points (5,7), (2,4), and (2,10), the sum is 3. b)
  1. These exams are weighted evenly, so the grades are perfect substitutes, so that the sum is all that matters. This means that the graph is a straight line with slope –1. d)
  1. Her utility was 15*19 + 5*5 = 310. So 310 = 15*14 + 5y, so 100 = 5y, so y = 20. c)
  1. Her utility was 12 + 4*5 = 32. So if x = 0, y must be 32. c)
  1. Factor the utility function into (x + 8w)2. We know that a monotonic transformation such as squaring preserves preferences, so that his indifference curves are the same as if his utility were just x + 8w. And x + 8w = constant is the equation for a straight line. b) For the skeptical out there, just find some points that fit and sketch it.