(Signaling) Prof. Li has an extra ticket to a major Sports event. He wants to sell it. but prefers to sell it to a person who cares about people in need. rThe ticket is worth $1000 to whoever he sells it to. A potential buyer approaches him. Prof. Li cannot tell whether this potential buyer is a caring person or not. but believes the probability he is to be 1/2. If the potential buyer does care. then donation to the charity yields him some utility. h-'Iore Specically. for every 81 he donates. he receives 50 cents worth of utility from being helpful for those in need. In effect. then. donating 81 costs him only 50 cents. On the other hand. for a person who does not care. donating 81 costs 31 since they do not get such utility from the donation. Prof. Li asks the potential buyer to donate. sees how much the person donates. and then sets a price for the ticket. If he concludes that the potential buyer is a caring person. he sets the price at 8200. If he concludes that the potential buyer is not a caring person. he sets the price at 8600. If he cannot tell. he sets the price at the expected value. 8400. The potential buyer knows all of the above. (a) Specify a separating equilibrium in which a caring buyer donates 8400. (b) Specify a pooling equilibrium in which a buyer donates 3100 regardless he is caring or not. (c) Is there a separating equilibrium in which a caring buyer donates S300? Explain. (d) Is there a pooling equilibrium in which a buyer donates 8300 regardless he is caring or not? Explain