Foreword
This was a short homework essay I had to write for my Economics class in the lower sixth. NHS stands for the National Health Service, the provider of free healthcare in the UK. This is an economic argument. I have studied the subject to a reasonably high level, however I'm sure some of you degree-level economists could correct me on a few points. Apologies in advance for any errors or lack of clarity.
Please also note that this same argument (or variants) can be equally used to explain the higher wages of other unique goods such as other musicians, sports stars, actors, etc. I believe my teacher chose Madonna because as an opera lover he found the success of such a talentless person (in his eyes, of course) rather distasteful.
The Essay
Madonna earns vast sums of money each year as a pop star, while British nurses are considered to be amongst the most underpaid workers in the country. One could argue that the amount of talent they possess and the amount of effort they put into their respective jobs is equal at best, but almost certainly in favour of the nurses. This begs the question, why does Madonna earn so much more than all the nurses?
The key difference between Madonna and a nurse is that Madonna is a unique good. There is only one Madonna, yet there are thousands of trained nurses, and even more people capable of entering the nursing profession. In the music industry there are no direct substitutes for any artist or band as they are all unique. Skilful marketing has created a specific image of each artist which results in brand loyalty. Even if a "better" singer emerges, Madonna has the advantage of brand loyalty, and will therefore continue to sell records and concert tickets for as long as she performs.
This brand loyalty that Madonna has generated makes her an attractive prospect for record companies - they will sell many more records if they are sung by Madonna than if they were sung by Josephine Bloggs. This means that Madonna is heavily demanded by record companies who know that signing her up will be hugely profitable for them. As she is a unique good, she essentially has monopoly power - there is no direct substitute for her, so she can set as high a price (recording contract, wages, takings from concerts, etc.) as she likes (within reason, and assuming continued popularity).
A nurse will often only have nursing qualifications and a strong desire to nurse people. They basically have only two options - working in NHS hospitals, or working in private hospitals. Private hospitals are relatively low in size and number, so many nurses are forced to work for the NHS. This high number of potential employees and very low number of potential employers is weighted heavily in favour of the employer. They will control the wages, therefore the nurses are paid low wages. In addition to this, each individual nurse does not represent a huge benefit to the NHS, whereas Madonna represents a massive increase in profits for any record company that signs her up. She is not the active party in the employment process - she already has a brand image and loyalty, and a proven record of generating revenue. This means that she is free to demand high profits as record companies fight to secure a recording contract.
e-hadj adds that the other major factor at play here is that the NHS are a near-monopsony on nursing services. | 
