It was all backslapping joy last week when Mayor Ed Lee signed the city’s budget for the 2016-17 fiscal year. Handing out silver pens to the key players, the frugal mayor assured onlookers they were actually very cheap pens.

“Having worked hard on the way we do our budgets and the way we conduct ourselves at City Hall financially, we’re in the strongest financial position in the history of the city,” Lee announced from the balcony outside his office.

We’ll say. The city’s new record-busting budget totals a whopping $9.6 billion — yes, billion with a b.

That’s more than twice the net worth of Donald Trump, according to Forbes. It’s bigger than the budgets of 13 states, including Iowa and Alaska. It’s enough to buy million-dollar homes for every public school teacher, police officer and firefighter working in San Francisco — with a couple billion left over.

But it’s not enough, at least if the November ballot and its roster of revenue measures is any indication. That’s right, San Francisco. The people in charge of our $9.6 billion want more money.

The biggest tax measure before voters in November is a three-quarter-cent sales tax increase that would raise $150 million a year — $100 million for transit improvements, and $50 million for homeless services and housing. Lee and the majority of the supervisors support it.

A tax on sodas and other sugary drinks would raise prices by a penny per ounce. Designed with the hope of curbing obesity and diabetes, the money would go into the general fund.

Homeowners would also see their parcel taxes go up by $20 a year to benefit City College if another measure passes. The current parcel tax charges homeowners $79 a year for the institution, and it expires in four years. The new measure would up that amount to $99 a year through 2032. It would pay for faculty raises, libraries, technology and other basics.

The San Francisco school board will ask voters to approve an eye-popping $744 million bond measure to build a school in an undecided location, improve existing facilities, make technology upgrades and build an arts center on Van Ness Avenue. It would also include $5 million for affordable teacher housing, something the district has pledged to build for more than a decade but still hasn’t.

Then there’s a measure to set aside $19 million annually to hand back responsibility of street tree maintenance to the city, which during the recession had turned the job over to homeowners. That measure wouldn’t raise taxes, but it would leave less money available for other services.

There’s a similar measure to set aside an increasing amount of money for senior citizens services, another to dedicate hotel tax revenue to artists and homeless families, an increase in the transfer tax when properties worth more than $5 million change hands, and a $3.5 billion regional bond measure to pay for BART improvements.

Everybody likes old people, trees, artists, schools, trains that are clean and run on time, and sidewalks that aren’t filled with tent encampments. But why can’t they be paid for with $9.6 billion?

First, some structural reasons. City College, the San Francisco Unified School District and BART maintain budgets separate from the city, so their requests wouldn’t come from the $9.6 billion anyway.

Also, San Francisco is both a city and a county, so those billions also cover the airport, San Francisco General Hospital, the port and the Hetch Hetchy water system. The general fund — which pays for standard city services like, in theory, street tree maintenance — totals a mere $4.8 billion. (Still, that’s a bigger budget than South Dakota’s!)

In addition, the city’s tech boom has meant not only more revenue for the city, but also more people living here who need those services.

“The mayor and the board have worked to not only restore services cut during the last recession, but to grow them in certain areas to service a growing population,” said Controller Ben Rosenfield, pointing to the increase in affordable housing spending as an example.

The same economic factors that make life in San Francisco more expensive for all of us make it expensive for the city, too.

“Costs are increasing across the board on most things, and revenues are growing too but not quite as quickly,” said Melissa Whitehouse, the mayor’s acting budget director.

The cost of paying the city’s 30,751 employees increased by 6.5 percent from last year due to labor negotiations. Everything from building maintenance to technology has gotten more expensive, too.

Rosenfield and Whitehouse agreed there would be no way to pay for major new enhancements to city services, such as $50 million for homelessness and $100 million for public transportation, without additional revenue.

Supervisor Mark Farrell, the board’s budget chair and a backer of the sales tax, said he does understand constituents’ concerns about big-spending government officials asking for more money.

“As a fiscal conservative, it’s taken quite a while to come to terms with it, but it’s something I very much believe in,” he said of the necessity of the sales tax increase.

Supervisor Katy Tang, perhaps the most fiscally conservative member of the board, said she hears from her Sunset District residents about their taxes being too high. She said that in good times, City Hall tends to hire more staff and create new mandated set-asides of cash, like the ones for seniors and trees, and create new programs.

“Over time, a lot of things have been layered onto our budget, and it’s really hard to go in and take them away,” she said. “It ties your hands for future budget seasons.”

Rafael Mandelman, a trustee of the City College board, said it makes sense to try to tap the city’s huge amounts of private wealth to pay for public problems like underfunded schools.

“You can’t manage those public problems without money,” he said. “The mere fact that you’re spending a lot of money on something doesn’t mean you’re spending what you need to on it.”

It seems most city elected officials agree — at least somewhat. As Lee finished signing the new budget last week, he declared, “Let’s go to work — don’t waste time, don’t waste money!”

He didn’t add, “And please give us more!” But he might as well have.

Heather Knight is a San Francisco Chronicle staff writer who covers City Hall politics. Email: hknight@sfchronicle.com Twitter: @hknightsf