As a typical student, suppose that you buy a ballpoint pen every month at price $0.5. But this time, you see a gel pen X on the counter. While you are willing to pay up to $2 for a high quality gel pen that does not drip, you are willing to pay nothing for a low quality one. Your initial belief is that gel pens are high quality with probability 0.3. You know that a high quality pen costs $1 but a low quality pen costs (virtually) nothing to produce. Assume that both you and producers have a discount factor δ = 0.9. Also assume that each product stays on the store counter for T 1 months.
(a) Would you buy the gel pen if it were priced at $1?
(b) Can producer X signal (high) quality through its first month price?
(c) If X spends $A in advertising per pen and posts a first month price of $1, for what values of A will you buy its gel pen?