The 66-year-old, of Ballybinaby, Hackballscross, County Louth, faces nine tax charges at the Republic of Ireland's Special Criminal Court.
Prosecutors claim he had significant dealings in cattle and land and received farming grants but failed to submit tax returns for nine years.
Mr Murphy denies the offences.
His defence lawyers claim that their client's brother, Patrick Murphy, managed his cattle herd and farming activities.
The prosecution at the three-judge, non-jury court was brought after an investigation by the Irish Criminal Assets Bureau (CAB).
One of the judges indicated that the verdict may be delivered next Thursday, 17 December, but added it is "by no means certain".
Mr Murphy was remanded on continuing bail until 17 December.

Reserve Bank of India governor Raghuram Rajan hinted that using cheap money to tackle economic problems - rather than painful reform - had to stop.
And he warned said that more intervention by central banks now risked doing "more harm than good".
Mr Rajan accurately predicted the global financial crisis in 2008.
In an exclusive BBC interview in Mumbai he said:  "I have been a little concerned about the immense burden for action that is falling on central banks and I think it is quite legitimate for central banks to say at some point  we can't carry the burden ourselves in fact we may not have the tools to do everything that is asked of us."
"Don't keep asking us to do more because at some point we get into territory where the consequences may be more bad than good if we actually act."
Mr Rajan acknowledged that his situation was not typical in the current climate, because unlike most global economies, India still has high inflation - running at close to 6%. Interest rates are also high - at  7.25% despite having been cut three times this year to try and stimulate growth.
"In my country I'm faced with traditional central bank problems like inflation so we still have a handle to work with those," Mr Rajan said.
He added: "But in some other countries you are faced with problems which are maybe way beyond what the central bank is capable of addressing such as demographic change, deep changes in productivity - and those are probably best dealt with other tools.
"But if the other tools aren't being used or there's a sense they'll take too long to work and you're working with the central bank only as the primary engine you may end up in situations that actually create more harm than good.
"Once interest rates are at zero it's hard to crank up new tools. Central banks have tried, they've tried very hard - negative interest rates,  low for long, quantitative easing, we've done a whole bunch of things like that.  The question is - at what point do you, through additional measures, do more harm than good?"

There may be clashes, but a series of deals between Labour and the government have defused most of the big problems in advance. I've lost count of the number of times Labour's point person, Keir Starmer uttered the words: "I am grateful for that indication," as the Security Minister John Hayes announced changes.
Today's big compromise announcement will be the composition and remit of the panel which will assess the operational case for the powers, under the leadership of the independent reviewer of terrorism legislation, David Anderson QC.
This matters because the panel have to report by the time the bill reaches committee stage in the House of Lords, and if they called for significant changes that would be pretty hard for ministers to resist.
That follows on from the government accepting special protections for Trade Unions and from a government "manuscript amendment" on the role of the "Judicial Commissioners" who would co-sign warrants for investigatory powers - which would allow them to scrutinise the facts of the case, not just the reasonableness of the process by which a warrant was issued.
In both cases Labour got pretty much everything they asked for.
Further compromise may well emerge on the issue of keeping internet connection records and the level of access to them, and on the protection of medical records. Protection of journalists and their sources seems a tougher issue - although some suspect that the government would like a few compromise-able issues in its back pocket, so that it can throw a few bones to their lordships, when the bill is considered in detail in the Upper House.
I suspect Labour will probably vote for the bill at tonight's third reading - perhaps with a few reservations, while the SNP and probably the Lib Dems will oppose.
And then the action switches to the Lords.
The trial of the prominent republican Thomas "Slab" Murphy for alleged tax evasion has heard the court may deliver judgement on the case next week.
[NEXT_CONCEPT]
Central banks are under too much pressure to fix struggling economies, according to the man in charge of India's monetary policy.
[NEXT_CONCEPT]
Day two of MPs' detailed consideration of the Investigatory Powers Bill - and the issues of the day should be the retention of internet connection records and protection of medical records and journalistic privilege.