Son of Alexander Murray, 4th Lord Elibank and Elizabeth Stirling. Married (1735) to Maria Margaretha de Jonge (d. 1762), daughter of Cornelis de Jonge van Ellemeet and widow of Lieut-General William North (1678-1734), Lord North and Grey. A sometime member of the Cocoa Tree Club. Member of The Poker Club.
A brilliant man of great knowledge he wrote Essays on Paper Money, Banking, etc. (1755) Thoughts on Money, Circulation, and Paper Currency (1758), Inquiry into the Origin and Consequence of the Public Debts (1758/9), Queries Relating to the Proposed Plan for Altering Entails in Scotland (1765), Letter to Lord Hailes on his Remarks on the History of Scotland (1773) and Considerations on the Present State of the Peerage of Scotland (1774). Alexander Carlyle, in his autobiography, described Lord Elibank as one of the most learned and ingenious noblemen of his time, and as having a mind that embraced the greatest variety of topics and produced the most original remarks.
Boswell was with Murray on November 26, 1762 at Lord Eglinton's in London, describing him as a man of great genius, great knowledge, and much whim. Boswell had a conversation with Lord Elibank in the company of Lord Eglinton, James Macdonald and Thomas Sheridan.1
Boswell and Dr Johnson also visited the Lord Elibank during their 1773 tour of the Hebrides.
Few (virtually none) of Patrick Murray, Lord Elibank's writings are generally available today, although searches at AbeBooks for Lord Elibank may turn up something.
Lord Elibank as frequently mentioned in Alexander Carlyle's autobiography, The Autobiography of Dr. Alexander Carlyle of Inveresk, which is fairly easy to come by.