Economy isn't the only reason India matters to Britain. There's also its democracy with its three million elected representatives — a beacon to our world.

It's a real pleasure to be back in India. This is my third trip here and with each visit, time seems to have leaped forward by decades in just a few years. It is exhilarating to see a country growing at super-speed before your eyes. But I'm not just here to enjoy the energy of this country. I'm here with a very clear purpose: to renew the relationship between India and Britain — to re-launch a relationship that is stronger, wider and deeper. Both our countries have talked about it long enough. Now it's time to turn those words into reality.

To show how serious I am, I have brought with me the biggest visiting delegation of any British Prime Minister in recent memory: members of my cabinet, industry leaders, top businessmen and women, figures from the arts, sports and local government. We're all here to make the case that this deeper relationship will be beneficial not just for our own countries, but for the world.

From the British perspective, it's clear why India matters. Most obviously, there is the dynamism of your economy. In the U.S., they used to say: “Go West, young man” to find opportunity and fortune. For today's entrepreneurs, the real promise is in the East. But your economy isn't the only reason India matters to Britain. There's also your democracy with its three million elected representatives — a beacon to our world. There is your tradition of tolerance, with dozens of faiths and hundreds of languages living side by side — a lesson to our world. And there is this country's sense of responsibility. Whether it's donating reconstruction assistance to Afghanistan, peacekeeping in Sierra Leone or providing intellectual leadership in the G20, India is a source of strength to our world.

So it's clear why India matters to Britain. But why should Britain matter to India? I believe our two countries are natural partners. We have deep and close connections among our people, with nearly two million people of Indian origin living in the U.K. We share so much culturally, whether it's watching Shah Rukh Khan, eating the same food or watching cricket. Beyond the cultural bonds, Britain has practical attractions for India. We speak the world's language. We are still the world's sixth largest manufacturer and the best base for companies wanting to do business in Europe. We have some of the best universities in the world and we are a great hub for science and innovation. Britain still has the strengths of its history, not least our democracy, rule of law and strong institutions, but there is also the modern dynamism of the nation that helped pioneer the internet, unravel the DNA code and whose music, films and television are admired the world over. All of these things can mean opportunity for Indian investors and entrepreneurs.

So if these are the foundations of a stronger relationship, how can that relationship benefit our countries and the wider world? I believe there are three global challenges we must take on together.

The first challenge is economic. In the past couple of years, we have seen global economic turmoil. Now both our nations must ask how we can emerge from the storm stronger and more prosperous. We come at this challenge from very different angles. On any measure, India's economy is on an upward trajectory. In Britain, we're waking up to a new reality. For centuries my country assumed we could set the global economic pace. But economic power is shifting — particularly to Asia — so Britain has to work harder than ever before to earn its living in the world. I'm not ashamed to say that's one of the reasons why I'm here in India. I believe that to spread opportunity for all our people, from Delhi to Dundee, Bangalore to Birmingham, we would benefit from a common strategy for economic growth.

We must start by making our own economies as open and dynamic as possible. That's why within fifty days of coming into power, our government introduced an emergency budget to cut red tape, reduce corporation tax rates, improve our infrastructure and show that Britain is open for business. Next, both India and Britain must encourage more investment from each others' countries. Companies like Vodafone, Wipro and Infosys are showing the way — now let's go further. Yes, that means bringing together the best and brightest from both our countries through scholarships and by twinning universities. But it also means doing the more difficult thing of opening up our own economies to foreign direct investment. We have welcomed your expertise in car manufacturing and steel production; and we need you to reduce the barriers to foreign investment in legal services, defence, banking and insurance.

But perhaps the biggest economic boost of all will come from more trade. EU-India trade is worth £50 billion a year already — and I'm determined we expand that by sorting out an EU and India Free Trade Agreement by the end of the year. We also need to hammer out a global deal. Agreement on Doha would add $170 billion to the world economy. Together we need to make the argument that we will only get things moving on Doha if we expand it — because when the pie gets bigger, we'll all get a greater share. So let's demonstrate our commitment by opening up our economies and showing we mean business.

The second challenge we must meet together is ensuring global security. Both India and Britain have suffered grievously at the hands of terrorists. We've worked together in the fight against terrorism before and I'm here in India to propose an even closer security relationship. This year and in 2012, Delhi and London are hosting the Commonwealth and Olympic Games. It makes sense that we co-operate closely to ensure both are as safe as possible. It also makes sense for us to share expertise on defence technology — as we've seen with the building of Jaguar and Hawk aircraft in India in recent decades. And when it comes to the security of our people, we cannot ignore what's happening in Afghanistan and Pakistan. Let me be clear: India's relations with those countries are a matter for you — and you alone. But because when we both want to see a Pakistan free from terror, when we both want to see an Afghanistan that is secure in its own right, again it makes sense that we work together to realise those interests.

The third challenge we must meet together is climate change. Decisive action is long overdue — and that must be global action, with all major economies playing their part. It's only fair that those with the longest history of carbon emissions make the biggest contribution to this. But it's also fair that the largest polluting countries contribute too. Indian action is of course different to U.K. action. We know that India's development needs mean that its energy needs and carbon emissions will have to grow. But by working together, we can help you avoid some of the high carbon mistakes we made.

So this is the case I'm making for a stronger, wider, deeper relationship between India and Britain. I have come to your country in a spirit of humility. I know that Britain cannot rely on sentiment and shared history for a place in India's future. Your country has the whole world beating a path to its door. But I believe Britain should be India's partner of choice in the years ahead. Starting this week, that is what we are determined to deliver.

(David Cameron is British Prime Minister.)

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