Regulation of monopoly. A monopoly has the cost function qix where θi is constant marginal and average cost and x is output. The monopolist may have either high costs (q1) or low costs: q2  q1. The...

Regulation of monopoly. A monopoly has the cost function qix where θi is constant marginal and average cost and x is output. The monopolist may have either high costs (q1) or low costs: q2  q1. The regulator cannot observe the monopolist’s type. Consumers’ gross benefit from the product is B(x) and their demand for the product is determined by B′(x)  p where p is its price. The regulator can control the output of the monopoly. (Having decided on a particular output she just sets the price at p  B′( x).) She can also make a transfer T 0 to the monopolist. The transfer must be financed by distorting taxation elsewhere in the economy and has net social cost of kT(k  0). The regulator’s welfare function is B(xi)  qi xi  kTi . She believes that the probability that the monopoly is high cost is p. The monopoly’s objective function is just operating profit plus the transfer and it will close down if this is negative. What is the optimal regulatory regime (x1, T1, x2, T2) and what prices will result? What is the optimal regime if transfers have no social costs (k  0)?