A firm's has quality {0,....,100}, each of which is equally likely. Regardless of , with

Probability 1/10, the firm can only send message m = ; while with probability 9/10 it can send

one of two messages m = or m = . Consumer observes the firm's message and forms a

belief about the firm's expected quality b = E [|m]. The firm wants to maximize b, i.e., it

wants to maximize the consumer's expectation of its quality.

Note the distinction between 0, which is a potential value that can take and , which is

not a potential value for but rather a message that is "silent" about .

Is there an equilibrium with a cutoff type ^* such that: (i) every firm with < ^* sends a

message m = , (ii) every firm with ^* sends a message m = if it can? If so, what is

^*?