Deficits do not cause inflation. It's the printing press--when you create money in excess of need you get inflation. When you try to fund it without getting the money from somewhere you run the printing presses fast and the money supply goes up--inflation goes up. You have to keep going ever faster to keep from falling off. Hyperinflation.
I'm at a loss. I don't understand that at all. Maybe you could try to explain it.
If you ran the printing press but didn't run a deficit, how would that create inflation?
What do you mean by "need," "when you create money in excess of need"?
Isn't running a deficit the same as "try[ing] to fund it without getting the money from somewhere"?
Society has a supply of goods & services. For the sake of argument the combined value is $1B in current dollars, the people have $1B in money to buy them. The government wants 10% of this but doesn't want to tax. So they print $100M and go buy goods.
Next round: Now there's $1.1B in money, but still the same $1B in goods. People spend their $1.1B but get only $1B in goods--prices went up 10%. The government still wants 10% of the market, now they have to print $110M to get it.
Next round: $1.21B in money, prices went up another 10% for a total of 21%, the government has to print $121M.
Next round: $1.331B, another 10% for a total of 33%, the government prints $133.1M
Next round: $1.4641B, total of 46%, print $146.41M
Next round: $1.61B, 61%, $161M.
Prices double in only 8 rounds. Note that tax revenue lags, the government takes in less than the tax rate would indicate, thus they need to print even more to compensate.
I talk about "in excess of need" because the economy needs a supply of money. In this case, we had the $1B. Note that in the real world the government's control of the supply of money is limited. The government can decide how much money to print but it has only a limited control on how that is spent--but from the standpoint of inflation it's the number of spending incidents that count, not the number of dollars. The same dollar typically gets spent several times a year.
Note, also, that in times of hyperinflation dollars lose value quickly, people spend them as fast as they can--greatly increasing the rate they move around and thus the money supply. If we go from spending a dollar once a month (because the majority of our bills are monthly) to weekly the money supply goes up 4x--if nothing else changes you get 400% of inflation.
This is why the government normally doesn't try to control the money supply by printing, but by interest rates--when interest is low there is more borrowing and money moves faster. With the housing collapse we saw the government peg this control and it wasn't enough, they responded by in effect using the printing press (electronically, not physical cash) to inject more money into the system. This is a dangerous move because if the economy recovers faster than you can pull the extra back out you'll get inflation.
Debt doesn't do this because debt in effect adds another good to the market--the debt instruments. The government spends the money but pulls it back out with the bonds, the amount of money moving around remains the same and you don't get inflation.