Energy and environment ministers from the world's major economies are meeting in London today to try to accelerate crucial negotiations over an international treaty on climate change.

Strong progress has been made in the past few weeks, with Japan, for example, announcing that it will cut its emissions of carbon dioxide and other greenhouse gases by 25% by 2020 relative to levels in 1990.

But there are still major obstacles and some doubt whether a strong global deal can be hammered out in time for the United Nations's conference on climate change in Copenhagen, now just seven weeks away.

Agreement can be reached if governments now focus on the key issue: the required overall reduction in emissions, with rich countries taking the lead through strong, binding targets and financial support for developing countries. Numbers are important to this, so let me explain why.

Global emissions of greenhouse gases in 2010 are likely to be about 47bn tonnes of carbon-dioxide-equivalent (they may have exceeded 50bn tonnes without the global economic slowdown). Countries around the world have been designing programmes that could reduce annual emissions to about 49bn tonnes of carbon-dioxide-equivalent in 2020, compared with 55 to 60bn tonnes under "business as usual".

However, to have a reasonable chance of cost-effectively limiting a rise in global average temperature to no more than 2˚C, beyond which scientists regard as "dangerous" to go, annual emissions must be reduced to below 44bn tonnes by 2020, well below 35bn tonnes in 2030 and well below 20bn tonnes by 2050.

Put another way, today's average world emissions per capita are nearly 7 tonnes of carbon-dioxide-equivalent each year, with big variations between countries: for instance, the United States emits about 24 tonnes per head while the figure for India is below 2 tonnes.

By 2050, the global population is projected to rise to 9 billion, so average per head emissions will have to be lower than 2 tonnes per year on average. For rich countries, this will require a cut in annual emissions by at least 80% by 2050.

But given that China's emissions are 6 tonnes per head and growing, and that today's developing countries will be home to 8 billion people in 2050, it is clear that they must also be at the heart of the action on climate change.

So we must find a further cut of 5bn tonnes on top of current intentions for 2020. This is achievable. For example, greater efforts on tackling deforestation could reduce emissions cost-effectively by at least another 2.5bn tonnes. International shipping and aviation could further reduce the global total by at least half a billion tonnes.

The rich countries could also reduce the global total by more than a billion tonnes if they implement their conditional "high-ambition" commitments – the European Union, for instance, will increase its cuts by 2020, relative to 1990 levels, from 20% to 30% if there is a strong global deal.

Developing countries could also make a similar contribution through finding improved ways of achieving economic growth while lowering their emissions per unit of output. In both rich and poor countries, there is great potential both from energy efficiency and new low-emissions technologies.

All of this can be achieved in the next decade with carefully designed policies. Indeed, if we set out strongly on this road we will create a new era of prosperity and growth. Innovators are full of ideas and investors see the opportunities. They now need confidence in strong international policy.

Many developing countries have already drawn up detailed plans for making the transition to a low-carbon economy and have taken significant steps forward in the last few weeks.

For instance, Hu Jintao, the Chinese president, announced last month at a United Nations summit in New York that his country will cut carbon dioxide emissions per unit of gross domestic product by a "notable margin" by 2020 compared with levels in 2005.

Jairam Ramesh, the Indian environment minister, last weekend outlined a series of important measures that his country intends to take across a wide range of sectors, including the goal of obtaining a fifth of its energy from solar, wind and hydro sources by 2020.

Rich countries must give their backing to these plans by providing developing countries with $100bn a year by the early 2020s, for measures to reduce emissions (much of which could be delivered by the operation of carbon markets), and a further $100bn to help them adapt to the effects of climate change that cannot now be avoided. Developing countries are likely to doubt the credibility of such commitments unless the rich countries also set an intermediate target of $50bn per year by 2015.

These sums must be over and above current commitments on official development assistance. They may appear large, but $200bn represents around 0.5% of the current gross domestic product of the rich countries, and is tiny compared to the risks that can be avoided by an international agreement. And it will not be possible to overcome poverty in poor countries without also tackling the threat of climate change: the global deal must be founded on a clear understanding that these two issues are closely bound together.

An ambitious deal on climate change that is effective, efficient and equitable is within our grasp, but only if our political leaders remain focused on the core common goals and maintain their determination to reach agreement.

Lord Stern is chair of the Grantham Research Institute on Climate Change and the Environment and IG Patel professor of economics and government at the London School of Economics and Political Science