Pension saving is on the increase in Britain. The rise has nothing to do with George Osborne's budget last week but is the result of employees being automatically enrolled in company schemes if they are over 22 and earn more than £9,440 a year.

Previously, employees had to opt-in to workplace schemes, so fewer did. Millions more will save for their retirement as a result of this relatively small change.

The former cabinet secretary Gus O'Donnell is a strong believer in behavioural economics. He says, for example, that the Treasury could vastly increase its tax take with a small change to the self-assessment forms sent out by Revenue and Customs.

At present, an individual fills in the form and on completion signs the form. Lord O'Donnell says the warning that false declarations can lead to prosecution should be put in big block capitals at the top of page 1. That would immediately alert people to the risks involved in trying to cheat the taxman and lead to billions of pounds of extra revenue.

This is an example of "nudge" economics. A shove in a certain direction can often have dramatic results. Humans are complex and don't always behave in the way economic textbooks say they should. Sometimes they override the rules of supply and demand. Sometimes they have to be persuaded by outside agencies to act in a certain way.

In France, there are around 15,000 growers of grapes for 66 champagne houses. The industry is geographically concentrated and the grapes vary little in quality. With this sort of homogenous product, you would expect each of the 66 houses to pay the same market price for its grapes.

Not so, according to a paper by Amandine Ody-Brasier of the Yale management school and Freek Vermeulen, of the London business school. The grape sellers have a certain idea of what a champagne house should look like, and are prepared to punish those that don't match up to expectations with higher prices for their raw materials.

What the growers like are houses run by a descendent of the founder, those located in one of the traditional champagne villages with a long history of producing bubbly. What they don't like are newcomers to the industry, those houses owned by a corporate group, those that supply supermarket brands, those that operate winemaking subsidiaries abroad, or those that try to buy their own vineyards. Moët & Chandon can expect to pay more for its grapes than Pol Roger because it is owned by the luxury brand conglomerate LMVH.

One grower quoted in the paper sums up the distaste for the arriviste houses. "Some of these firms, they come and go. Who knows for how long they're here, where they'll be in 5 or 10 years? They would leave tomorrow if they stopped making money. They don't care about champagne."

The paper shows that the price differences paid by champagne houses are quite substantial, with a gap of several euros at an average price of €9 (£7.5) per kilogram. Now, it could be argued that champagne is a special case. Global demand is rising and it can only be supplied from one area of France. Growers make tidy profit margins and can therefore afford to behave with Gallic disdain toward those for whom they do not care. But economics theory suggests that the growers will be seeking to maximise their profits rather than offering discounted prices to Krug simply because the house was founded in 1843. This is not the case, and it is the result of market forces being tempered by social norms rather than by a cartel. As the paper notes, "the prices different organisations are charged for their purchases depend substantially on whether they meet local expectations for who they are and what they do. Our qualitative evidence confirms that this differential pricing by growers occurs not through collusion but through a spontaneous bottom-up process."

For some reason, a Formula 1 grand prix ends up with the winner being drenched in champagne and it is the motor racing industry that provides the second example of how economics works. This time, though, the lesson (provided courtesy of John Llewellyn of Llewellyn Consulting) is about how regulation can prompt innovation.

Three years ago, the F1 authorities announced big changes to the rules governing engine size and fuel capacity. By this year, 2.4 litre normally aspirated V8 engines had to be replaced by 1.6 litre turbo-charged engines – a one-third cut in capacity. Simultaneously, fuel consumption – hitherto unlimited but averaging 160kg per race – had to be reduced to 100kg.

Lots of smart technologists and engineers work for the F1 industry and the new regulations forced them to find ways of making cars more fuel efficient without loss of power. They recognised that in an internal combustion engine only around one third of the fuel used actually propels the car, and went about recovering some of the lost energy.

As a result, this year's F1 cars have two new energy-recovery systems: kinetic energy released when Sebastian Vettel slams on the brakes is converted into electrical energy; and energy formerly lost through the exhaust is turned into electrical energy.

As Llewellyn notes, the boffins have done an amazing job. The old V8 engines produced more than 750 brake horsepower, but the one-third smaller V6 engines produce 600 bhp (only 20% less). In addition, the energy recovery systems are designed to provide an additional 160bhp for 33 seconds every lap. So the new engines will produce as much power as the old engines, using 40% less fuel.

This is not just a matter that should interest petrol heads. Llewellyn says applying this technology to everyday motor vehicles could cut global oil consumption by 2% or more a year. "But this F1 experience has a deeper significance: it shows what clever people can do when motivated."

Sometimes the motivation is money. Sometimes it is just plain curiosity. But quite often, clever people have to be pointed in the right direction. "This typically requires that government be involved: to identify the problem; specify it; corral key people; offer the prize; provide funding. Witness the second world war, which on that basis produced radar, radio navigation, the jet engine, rocketry and nuclear energy," Llewellyn says.

Could the same approach help in the fight against global warming? Yes, of course, but only under certain conditions. Governments have to be fully committed – as they are under war conditions and sometimes (the space race) in peace time too. They need to learn the lessons of auto enrolment, the champagne industry and F1. And be prepared to shove as well as nudge.