What is the definition of "Market Failure"?

Specifically, is the following Market Failure or something else?

        Consider a pharmaceutical company which develops a drug after the 
expenditure of say $1 billion and is able to produce a daily dose for 50 cents. 
 The company considers the volume to be sold and realizes that it must get, 
say, $5.00 per pill to make a profit.  The formula for the pill is public.  
Without a patent on the drug it can't sell for $5.00, so it needs patent 
protection to be profitable.

Is the need for patent protection "market failure" or is that something else?  

If something else, what is that called?

Gene
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