A monopoly sells to a market with demand D (p) = (2 ) where price...

 

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A monopoly sells to a market with demand D (p) = (2 − ²)² where price lies between 0 and 4. For any price above 4, demand is zero. The cost of the monopolist is zero, that is C(q) = 0 for all q. (a) (2 mark) Find the inverse demand curve of the monopolist. (b) (1 marks) Write out the profit as a function of quantity. (c) (1 mark) Is the second order condition for profit maximization satisfied? Explain. (d) (2 marks) Find the profit maximizing quantity and price explaining the method you use and why it is valid. (e) (1 mark) If the market was competitive, what price would be charged? A monopoly sells to a market with demand D (p) = (2 − ²)² where price lies between 0 and 4. For any price above 4, demand is zero. The cost of the monopolist is zero, that is C(q) = 0 for all q. (a) (2 mark) Find the inverse demand curve of the monopolist. (b) (1 marks) Write out the profit as a function of quantity. (c) (1 mark) Is the second order condition for profit maximization satisfied? Explain. (d) (2 marks) Find the profit maximizing quantity and price explaining the method you use and why it is valid. (e) (1 mark) If the market was competitive, what price would be charged?

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a The inverse demand curve is Pq 2 q Since the direct demand curve is Dp 2 p and taking the inve... View the full answer