18. Economics of Information

Information is itself a good — how much a signal improves a decision, and when to stop searching optimally.

• The Value of Information — Should you invest or not? A signal helps you decide. The more accurate the signal, the better the decision. After seeing the signal, you recompute the probability. A good signal says invest. A bad signal says stop. The value of information is the gap between deciding with it and without it. The formula below pins that gap down. For example, before buying a used 🚗 car, you ask an expert. The expert spots good and bad cars correctly 80 percent of the time. If the expert says good, you buy. If the expert says bad, you walk away. Your losses shrink a lot.
• Optimal Sequential Search — You visit shops one by one, hunting for the best price. Each extra shop costs you money. So you set one cutoff value in advance. An offer better than the cutoff, you buy at once. An offer worse than the cutoff, you keep looking. That cutoff is the reservation value in the formula below. For example, you shop around for a 👕 shirt. Each extra shop costs 1,000 won in 🚌 bus fare. You decide in advance: under 50,000 won, I buy immediately. At 60,000 won you walk out. At 48,000 won you buy on the spot.