US CAFE standard
In the 1970s, the United States government came up with Corporate Average Fuel Economy (CAFE). This said that each automaker had to hit a particular fuel economy standard measured as miles per gallon in average across the cars that it produced.
This had a number of effects:
It virtually ended a common car type, the station wagon. The station wagon was replaced by two new car types, the sport-utility vehicle (SUV) and the minivan. These new car types were larger and in some cases less fuel efficient than the cars they replaced. So why use them? They didn't fall under the same category for CAFE statistics. They went into the truck and van categories rather than the passenger car categories. By truck and van standards they were comparatively light and fuel efficient. But they were still as big or bigger than the station wagons were.
Cheap cars became more fuel efficient and their prices were subsidized by more expensive cars. But car makers had little incentive to make them last. In their ideal world, these cars would fail every year so that they could sell new high fuel economy cars to offset the profitable larger cars.
Older large cars became more valuable. They weren't covered by the fuel economy standards, so people who needed large cars continued using existing ones. This was bad, as older cars also were less fuel efficient than newer cars even when controlling for size.
Cars became less safe, as they removed material to make cars lighter. This was especially true of smaller cars.
People drove more. Because one tank of gas could drive farther and gas was cheap, people started commuting longer and longer distances. On average, people used the same amount of gas even though their cars were more fuel efficient. This had a number of additional negative side effects. For example, fewer people lived in cities, causing their tax base to fall. So the people in the city could afford fewer city services, which made even more people leave for the suburbs.
When you optimize for a different statistic than the one that really matters to you, you get improvement in the wrong statistic. Fuel economy was not what was important. Fuel usage was. But instead of taking measures to control fuel usage, like a gasoline tax, they optimized around one possible solution, fuel economy of new things arbitrarily classified as cars.
European gas taxes
Contrast this with what European countries saw with increased gasoline (which they may call petrol) taxes:
- Most older cars were junked, as they were too expensive to run.
- Cars were smaller.
- People took fewer or shorter trips.
- More mass transit usage.
It is of course conceivable that this was particular to Europe. But we know what happened when gasoline prices increased in the US from about \$1 a gallon to as much \$4 a gallon (before going back to the \$2.50 to \$3 range). Gas usage dropped precipitously and more people returned to urban centers. Pretty much the same as what happened in Europe.
There are about 3.79 liters in a gallon. However, in the 1990s, it was not strange for Europeans to pay about as much for a liter as Americans were paying for a gallon.
Yes, it is true that resource usage and economic growth are correlated. But the correlation is not one-to-one. In some cases, limiting economic growth might even hurt. For example, if most people can't afford a new car, then they will continue using their older, less fuel efficient cars. Thus lower economic growth may cause more resource usage than high economic growth. This is especially true if economic growth was high (so people could afford nice cars) and then drops (so people can't replace their cars).
Lack of economic growth may also cause public services to be cut. For example, mass transit often suffers during downturns. And again, less mass transit pushes more people to take trips in their cars.
If people are underwater in their mortgages (meaning that they owe more than the current value of the house), then it is difficult for them to move. So they're stuck in their current location and may have to travel farther to reach work or may have to turn down jobs that are just too far.
TL;DR: No, I would not expect this to work as desired.
What you really want is shaped growth. To some extent this will happen naturally. Allow people to speculate in resources. So someone who expects gasoline to increase in price will buy up and store reserves of oil for the future when it is more expensive. Let prices rise. This will throttle growth, but much less than playing with the money supply will.
I've focused on oil and gasoline because I know a fair bit about that example. But this works for other resources as well. For example, the real limiting factor with food is land. And people speculating into land in the hope that it will increase in value will lower the current utilization while allowing for future utilization. Or speculation in water rights.
If you really think it's necessary, the government can accelerate these changes by buying water rights, land, and mineral rights and not using them. This artificially restricts the amount of resources available.
Before doing that though, you may want to go through the system and look for ways that it encourages resource usage. E.g. property taxes encourage people to make the best use of their land they can. They effectively make speculating more expensive. It's one thing to buy low and sell high. It's another to buy low and then pay high maintenance taxes that eat up any profit from selling high. So shift from property taxes to resource taxes. Or something else that moves in the direction that you want to go.