Monopolistic signal provision

I study a monopolist who sells a signal to a consumer with a hidden type. The consumer uses this signal to obtain social status, defined as the expectation of the consumer's type conditional on the signal. The monopolist must decide how accurately different types are revealed. When pooling subsets of types, she reduces social surplus, but extracts greater information rents. I derive the optimal mechanism by examining the covariance between the consumer's type and his virtual marginal value of social status.