Im working on a Economics question and need guidance to help me study.
Hello can you please help me solve the below question?
A firms has quality x ? {0,
,100}, each of which is equally likely. Regardless of x, 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 = x. Consumer observes the firms message and forms a belief about the firms expected quality b = E [x|m]. The firm wants to maximize b, i.e., it wants to maximize the consumers expectation of its quality.
Note the distinction between 0, which is a potential value that x can take and ?, which is not a potential value for x but rather a message that is silent about x.
Is there an equilibrium with a cutoff type x? such that: (i) every firm with x < x? sends a message m=?, (ii) every firm with x?x? sends a message m=x if it can? If so, what is x??
Thanks!
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