What if you did a full-scale renovation of your house — but couldn’t afford to put the heat on or buy groceries once you moved back in? That’s the situation the state-run Metropolitan Transportation ­Authority could find itself in, unless Gov. Andrew Cuomo stands behind day-to-day labor savings to go with the MTA’s planned investments in its physical assets.

Last week, the MTA’s board approved a new five-year budget for the nuts and bolts of the agency. There’s lots to like: Of the $51.5 billion in planned upgrades, 79 percent will go to the city’s subways and buses. This is still not entirely fair, since subways and buses have 93 percent of ridership, while commuter rails have just 7 percent. But it’s much better than the last time around, when subways and buses got only 61 percent.

For whatever reason, Cuomo got his priorities roughly straight. The blueprint calls for $7.1 billion — the biggest single investment — in subway signal upgrades, including modernizing the signals on the Lexington Avenue line, which carries 1.6 million people a day.

“Advanced signaling can increase capacity on crowded train lines due to higher throughput,” the MTA notes. To allow for more trains per hour and replace obsolete cars, the MTA will spend $6.1 billion on 1,900 new subway cars, including 437 cars, or 40 new trains, for brand-new service. The MTA will expand its bus fleet, too, by 200.

And Cuomo is showing a commitment to finishing the Second Avenue Subway, with another $4.9 bill­­ion toward the $6.9 billion needed to bring it three more stops through Harlem.

So, lots of new service, on old and new lines — good. And the MTA is already demonstrating that when it does a better job, people will flock back to the system: Since January, subway ridership, after falling for three years, has stabilized.

Can the MTA realistically spend or commit $51.5 billion over five years, and do all the work it says it’s going to? Probably not. Of the current $30 billion, five-year capital plan for transit and commuter rail, which has only three months to go, the MTA has so far spent only $12.5 billion.

And is the MTA going to have trouble paying for these things, even with a projected $25 billion in new money from borrowing against the next few decades’ worth of congestion pricing and mansion tax revenues? Probably. Even after those revenues, and assuming an $11 billion contribution from Washington, it’s $10 billion short.

But the MTA has an even more pressing problem. Once it has built or bought all or some of these shiny new signals and trains, how is it going to afford to run them? In its $17.1 billion annual budget for regular expenses, like paying workers and buying fuel, the MTA faces a cumulative $740 million budget deficit over the next four years.

And that’s without a recession, which could devastate the MTA’s $7.4 billion in annual tax revenue and direct government subsidies, creating a single year’s deficit of $1 billion or more.

Already, even as the MTA prepares to buy buses to add service, it’s cutting back bus service in Brooklyn. It will slash afternoon frequency on the B46, the borough’s busiest line, from 20 to 12 buses an hour, to save $2.4 million.

The main culprit is high labor costs. The MTA will spend about $10.3 billion on labor next year, 60 per­cent of its total cash costs — set to rise to $11.1 billion in three years, one-third faster than inflation.

As a report privately prepared for the MTA in early summer showed, the average transit worker made nearly $134,000 last year — $89,000 in cash and the rest in benefits. New York City’s median household cash income is about $61,000.

Transit workers seem happy with their pay and benefits. Last year, only about 0.5 percent of the workforce quit, compared to 18 percent of people who work for large ­employers nationwide.

That’s no wonder. It’s really hard to get a transit job. The MTA hires about 2 percent of people who take the conductor’s test and 3 percent of people who take the train operator’s test. These jobs are harder to get than a Harvard education.

That’s fine, but this exclusive workforce has to show a little flexibility in its current round of contract negotiations with its employer — so the MTA can afford to run some of its brand-new subway cars and buses.

Nicole Gelinas is a contributing editor of City Journal.