You asked how, so I’m going to give you a couple of examples.
First, I think the ‘working harder under lower taxes’ answer is only partially correct. A more correct answer, but one I think a lot of people will disagree with because of their political beliefs, is this:
People who have high incomes have, on average, demonstrated that they are better stewards of money than people with lower incomes. This especially applies to investment capital, and which is why many supply-side advocates focus on capital gains and dividend taxes.
If Businessman A takes $1,000 and uses his superior knowledge to invest it in high-productivity uses, the economy benefits. If poor person B takes the same $1,000 and blows it on smokes and booze, it doesn’t. So some would argue that progressive taxation removes money from the most productive sectors of the economy and gives it to the least productive. I think there is some truth to this, but I don’t know how to quantify it.
Another effect is that higher taxes cause deadweight loss. In an undisturbed, well-functioning market, decisions are considered to be close to Pareto-Optimal (i.e. there’s no change you can make that will increase overall systemic efficiency). This happens because people will only trade if the marginal benefit they get from the trade exceeds the marginal cost. So prices fluctuate around until they find the point where the market clears, and this represents the optimum value for both parties in a trade.
Let me give you an example. Let’s say you, me, and Bob have $200 each, and we each have a widget to sell. We each also have a widget that we personally value at $100 (i.e. we won’t sell it for less), but which the other parties value more. So I go first, and put my widget up for sale. To you, it’s worth $150. To Bob, it’s worth $125. If we negotiate back and forth, I’ll eventually sell it for $150. The product went to the highest-valued use, and I got maximal value for it. Now Bob has something that you and I want. You’re willing to pay $140, but I’ll pay $145. So I buy it for $145. Now, you have an object that Bob and I want. I’ll pay $100 for it, but Bob will pay $130. So Bob gets it for $130.
Now, let’s add it up. Before we traded, between us we had $900 in value. After we trade, Bob has $215 plus a widget he values at $130. You have $180 plus a widget you value at $150. I have $205 plus a widget I value at $145. The total value in the system has increased from $900 to $1025, because our widgets added value when we traded them and put them in the hands of people who valued them more. That’s economic growth.
Now let’s add a sales tax of 30%. Let’s further stipulate that government is perfectly efficient and gives us all our money back with no losses. That should be a wash, right?
You still value my widget at $150. But if I sell it to you, I have to pay a sales tax of $45. Okay, I only make five bucks, but it’s still some profit. So the trade taxes place. In the second case, the sale is for $145, so Bob has to pay $43.50 in tax. That means he only gains $1.50 in profit. Okay, the trade takes place, but just barely.
The third trade, however, is different. Bob will pay $130. You value the widget at $100. If you sell it, you’ll pay $39 in tax. That means you’re losing $9 in value. So you refuse to trade with him, and the widget doesn’t find a higher-value use.
At the end of this little exercise, the government spreads the wealth around and gives us all our tax money back spread evenly among us. It doesn’t waste a cent. But our economy is $30 poorer because the tax stopped a value-added trade from taking place. That’s deadweight loss.
So higher taxes raise the threshold for value for trades. They force the trades on the margin out of the market, decreasing economic growth. It’s not just taxes that do this - it’s monopoly power, information asymmetry, or other flaws which prevent efficient markets.
This doesn’t prove the case that taxes always reduce GDP in a complex economy - perhaps there are other factors more important that the taxes correct. But that’s the theoretical reason why taxes create deadweight loss.
So, will reducing taxes cause government revenue to go up? That depends on two things - how much growth the taxes stimulate, and what kind of timespan we’re talking about.
For the sake of the argument, let’s say that at a fixed tax level growth is stable. Let’s say we have a 50% tax rate on income, which earns the government $1 million dollars. Let’s further stipulate that lowering the tax rate to 25% will cause a 10% increase in income per year. Discounting all other effects both positive and negative, this is what that looks like:
No tax cut case:
Annual Income: $2 million
Government revenue: $1 million
Total taxes collected after 10 years: $10 million
Total taxes collected after 20 years: $20 million
Tax cut case
First year income: $2 million
First Year government Revenue: $500,000
Second Year income: $2.2 million
Second Year government revenue: $550,000
Total government revenue: 1,055,000.
Third Year income: $2.42 million
Third Year revenue: $605,000
I think you see where I am going with this. When the rate of increase goes up, you get a geometric progression.
In this scenario, with the tax cut government revenue passes the steady state annual revenue revenue by year 9, and passes total revenue collected by year 15, at which point income is almost four times higher than it otherwise would be and annual revenue is almost double.
So that’s the theoretical case for how tax cuts can cause growth large enough to (eventually) offset the cuts. Whether the tax cuts really do cause revenue increases in a reasonable length of time depends entirely on your assumptions. If you don’t think tax cuts increase GDP growth, the answer is never. If you think they do, then the answer is “well yeah, at some point in the future”.
If anyone says tax cuts will cause revenue increases in the same year or even within a couple of years, they are either nuts or they’re looking at a different phenomenon, such as wholesale tax avoidance or a major shutdown of economic activity as a result of the tax rate. They could also be modeling things like taxes lost from income of workers if the taxes cause job losses. I believe this is the case with the luxury tax. It really hurt employment in the boat-building and aircraft industries, and the lost tax revenue from wages was greater than the tax collected on the goods. Thus, overall tax revenue went down almost immediately following a tax increase.