3. Banning Laptops - e for Students split their time in lecture between surfing the internet e and taking notes 1 utility u = 2(1 a)e+a(1 e) with relative preference for taking notes a [1/2,1). The professor cares acknowledges the benefits of surfing and note-taking, v = 2(1)e+(1e), but puts a larger weight = [a, 1) on the latter. The professor cannot directly control e, but he can ban laptops, enforcing e = = 0. a) Should the professor ban laptops? How does your answer depend on a and B. Give an intuition. b) Now assume that the student cares about note-taking because of her grade in a final exam, which depends on the time taking notes via (1 e) where X is the difficulty of the exam; so u = 2(1 a) e + a(1 e). The professor's preferences are unchanged. What difficulty should the professor choose? Should he still ban laptops? - c) The professor realizes that the exam is a noisy assessment, and the grade in the final exam is really given by (1 e+X) where X is mean-zero noise with variance V. The professor is risk-averse about noise in the grade with parameter r. Give an expression for the professor's equilibrium value as a function of . For high values of V, should the professor ban laptops? For low values of V, should the professor ban laptops?