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De Beers a monopolist is into the business of selling diamond which has a total cost function given as C = 1,200 + Q^2 and

De Beers a monopolist is into the business of selling diamond which has a total cost function given as C = 1,200 + Q^2 and an inverse demand function which is equal to P = 200 - Q. Where, Q is output, P is price and C is total costs.

a) Find the profit-maximizing output and price for De Beers. Is De Beers profitable?

b) Calculate the price elasticity of demand at the firm's profit-maximizing price and output.

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