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Consider a firm - Wotzits Inc - with two profit centres, A and B. In the firm, profit centre A makes one input at a marginal cost of $40 which it transfers for a price t to profit centre B. A is the only source of the input. B transforms one unit of input into one unit of output at zero marginal cost and sells as a monopolist into a market with a demand curve of P = 120 - q, where P is price and q the quantity of output. If both A and B act together to maximise profit for the firm, what is the final price, output and profit for the firm?

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