IAWYC, but the claims that most of the economic costs of elections are in political spending, and most of the costs of actually running elections are in voting machines are both probably wrong. (Public data is terrible, so I'm crudely extrapolating all of this from local to national levels.)

The opportunity costs of voting alone dwarf spending on election campaigns. Assuming that all states have the same share of GDP, that people who don't a full-state holiday to vote take an hour off to vote, that people work 260 days a year and 8 hours a day, and that nobody in the holiday states do work, then we get:

Political spending: 5.3 billion USD Opportunity costs of elections: 15 trillion USD (US GDP) * (9/50 (states with voting holidays) * 1/260 (percentage of work-time lost) + 41/50 (states without holidays) * 1/60 * 1/8 (percentage of work-time lost)) ≈ 16 billion USD

Extrapolating from New York City figures, election machines cost ~1.9 billion nationwide. (50 million for a population ~38 times smaller than the total US population.) and extrapolating Oakland County's 650,000 USD cost across the US's 3143 counties, direct costs are just over 2 billion USD. (This is for a single election; however, some states have had as many as 5 elections in a single year. The cost of the voting machines can be amortized over multiple elections in multiple years.)

(If you add together the opportunity costs for holding one general and one non-general election a year (no state holidays; around ~7 billion USD), plus the costs of actually running them, plus half the cost of the campaign money, the total cost/election seems to be around 30 billion USD, or ~0.002% of the US's GDP.)