684_s17_hw4a.pdf - Econ 684 J Sandford spring 2017 April 1...

Info icon This preview shows pages 1–2. Sign up to view the full content.

Econ 684, J. Sandford, spring 2017 April 1, 2017 Homework 4 answers Problem 1 A seller has a painting for sale that is either good or bad. A good painting is worth 1 to the seller. A bad painting is worth 0 to the seller. The seller knows the painting’s quality. The buyer does not know whether the painting is good or bad, only that it is good with probability 1 2 and bad with probability 1 2 . A good painting is worth v to the buyer. A bad painting is worth 0 to the buyer. The buyer makes a one-time offer to the seller, which the seller can accept or reject. To keep the problem simple, assume that the seller accepts offers where she is indifferent. a. Suppose v = 1. What offer should the buyer make? What is his expected profit? For all parts, if the buyer offers any amount in [0 , 1), his offer will be rejected, while any offer of at least 1 will be accepted. Given this, the only offers that could possibly be optimal for the buyer are 0 and 1. In part a, if the buyer offers 0, the offer is accepted iff the seller knows the painting to be bad, in which case the painting has no value to the buyer. Should the buyer offer 1, the seller will accept whether the painting is good or bad, meaning that the buyer’s expected utility is 1 2 * 1 + 1 2 * 0 - 1 = - 1 2 , so the buyer is better off offering 0. b. Suppose v = 1 . 5. What offer should the buyer make? What is his expected profit? An offer of 0 nets the buyer utility 0, while an offer of 1 gives the buyer expected utility 1 2 * 1 . 5+ 1 2 * 0 - 1 = - . 25. The buyer is better off offering 0 (and thus not getting the painting if it is good). c. Suppose v = 5. What offer should the buyer make? What is his expected profit? An offer of 0 gives the buyer utility of 0, while an offer of 1 gives 1 2 * 5 + 1 2 * 0 - 1 = 1 . 5. Thus, the buyer will offer 1, and will purchase the painting regardless of whether it is a good or bad painting. d. What is the lowest value of v such that both types of the painting are traded in equilibrium? v = 2. e. Discuss the efficiency of the outcome in a., b. and c. What is the source of the inefficiency, if any? The outcomes in part b is inefficient, since regardless of the quality of the painting, it is worth more to the buyer than the seller ( v > 1), yet the good painting is not traded. In part a, the painting has the same value to either the buyer or the seller, so it is efficient either for the painting to remain with the seller, or for a trade to take place. The outcome in part c is efficient, since the painting is worth more to the seller than the buyer, and both types of painting are traded.
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

Image of page 2
This is the end of the preview. Sign up to access the rest of the document.
  • Spring '11
  • JosephHarrington
  • Game Theory, player, J. Sandford

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern