Mr Hogg said accepting the Government's tax freeze deal would damage frontline policing in the Westcountry.
The force has already shrunk from 3,500 to 3,100 officers, while more than 500 police staff have also been lost, since Government cuts were imposed two years ago.
And it had been forecast that numbers would decline even further by 2016 to just over 2,800 – a level last seen in the 1980s.
But in detailed budget proposals tabled last night, Mr Hogg outlined how with an additional 2% from the taxpayer he could maintain police officer numbers at more than 3,000 while also retaining 380 community support officers and recruiting an extra 50 "specials" a year.
His 2% proposals fly in the face of pressure from Ministers to keep bills down.
However, Conservative Mr Hogg said accepting the Government's offer of freezing council tax in exchange for a 1% increase in grant, would leave the force facing a "fiscal cliff" in two years' time and an annual shortfall of £1.8 million.
"The impact of this option would be that I would be unable to deliver the police and crime plan," his report said.
"There would be a critical reduction in pro-active crime reduction, there would be a critical reduction in partnership, community and early intervention activity (and) there would be a critical reduction in police visibility and hence reassurance to the public."
If approved by the Devon and Cornwall Police and Crime Panel, which is charged with holding Mr Hogg to account and meets a week today, the police share of council tax bills for Band D properties would rise by £3.19 to £162.92 a year.
"Until this year's settlement the force have been assuming officer numbers would reduce to just over 2,800 by 2016," Mr Hogg's report to the panel said.
"In that scenario, once the force have calculated minimum response and CID levels, only 125 staff would be available for neighbourhoods.
"The chief constable has concluded that there is no credible way of spreading 125 staff over 4,000 square miles and still provide an effective neighbourhood presence.
"Furthermore, the chief constable believes that at that level he would have to withdraw from proactive crime prevention work, significantly reduce local visibility (and) withdraw support from local partnership and community groups.
"This budget proposal provides an alternative, providing for the maintenance of police officer numbers at over 3,000 for the next four years, and a real opportunity to maintain those numbers beyond that point."
Mr Hogg said he wants to "arrest the decline in police officer numbers" and "maintain visibility especially in rural areas".
Devon and Cornwall Police has been faced with making budget savings of £50 million in the four years to 2016 to meet Government cuts.
While hundreds of police officers were being forced to retire, crime in the two counties spiked by an unprecedented 7% – a trend which is now being reversed.
The pensions regulation, which compulsorily made officers retire after 30 years' service, was suspended last September after greater savings were achieved than had been expected.
That trend is thought to have continued and given Mr Hogg more financial flexibility in his first budget.
He is also proposing to use £4.3 million from reserves to top the total budget up to £288.6 million.
The police and crime panel, which is made up of local councillors and some independents, meets in Plymouth on February 8 when it will also discuss the appointment of Shaun Sawyer as the force's new chief constable.
The committee has the power to veto Mr Hogg's proposed budget and his choice of chief constable.
