Oprah is trying to decide how to allocate a 15-minute segment between two guests on an upcoming show. Pauly Shores antics start to wear thin fast; her marginal utility from his appearance is given by MU = 500 – 20T, where T is the number of minutes Pauly is on. (So, the first minute Pauly is on gives Oprah 480 utils; the second minute, 460; and so on.) Tony Randall, however, is always a solid guest. Oprah can count on him for a constant 200 utils every minute he is in front of the camera. Pauly demands $200 per minute for his appearance; Tony is happy with $100 a minute. To maximize her utility, how much time should Oprah give each guest?
Oprah can maximize utility when the ratio of marginal utility to price charged is equal among the two, i.e. (500-20T)/200 = 200/100 = 2, i.e….
500-20T = 400, i.e. 20T=100, i.e. T=5. Hence Oprah should give Pauly 5mins and Tony 10 minutes.