Mumbai – Arriving at the new international airport here last month, I felt like I had gotten on the wrong connecting flight and ended up in Shanghai. Instead of the smelly and decaying terminal I remembered from the four years I spent here as a news correspondent, the building was sparkling. The walkway to the immigration counter doubled as a museum filled with paintings, sculptures and handmade crafts from around the country.

But the old familiar India soon returned when my cousin drove me out of the parking garage and past the slums near the airport that were made famous by Katherine Boo’s book, “Behind the Beautiful Forevers.” Stunning wealth and wrenching poverty have always coexisted here. And it still does — despite the unbridled optimism of politicians, business executives and middle-class Indians about the kind of economic transformation symbolized by Mumbai’s airport. I spent a week listening to such talk. Everybody was sure things would change for the rest of India just as they had for the airport because the party of Prime Minister Narendra Modi, a technocrat with a controversial past, had captured a landslide election victory last year.

The rest of the world is also hopeful about India. The World Bank and the International Monetary Fund are projecting that India will become the world’s fastest-growing major economy in the next several years, surpassing China. The Indian government said this week that its economy may already be growing as fast or faster than China’s.

It is inevitable that India will eventually grow faster than China for the simple mathematical reason that it is easier to make a small economy bigger than it is to increase the size of a larger one. China’s economy was more than twice as big as India’s in 2013, after adjusting for population and purchasing power, according to the World Bank. Also, China’s population is aging and its labor force is shrinking whereas about half of Indians are 25 or younger and its work force will be expanding for many years to come.

What is less clear is the kind of an economy India will have. Will it be one that caters to the small elite that can afford air travel, or will there also be money and room for decent, affordable housing with running water and round-the-clock electricity? A recent report found that the country has the largest number of billionaires after the United States and China. Yet roughly half the population is stuck in subsistence farming, hoping for better futures for their children. Those young people receive such a lousy education that many businesses consider them unemployable. Many Indians recognize their country’s unique challenges, which will take years to address successfully even as others hope for revolutionary change. I struck up a conversation with a working-class man I met in the northern city of Jaipur, Chhagan, who only identified himself by one name. I asked him if he thought Mr. Modi would make India better, he said: “Modi is a good man, but he is just one man.” At the Jaipur Literature Festival being held nearby, corporate executives, analysts and government officials offered a more upbeat assessment. One session was titled “India’s Turn: Catalyzing Economic Transformation.”

Mr. Modi’s government, in office for less than nine months, has already raised expectations significantly among investors and ordinary people by promising to turn the country into a latter-day China with bullet trains, 100 new “smart” cities and tens of millions of manufacturing jobs.

But there is growing frustration that the change he promised might not come soon enough or that it might be disrupted by some of his fanatical right-wing supporters. Nearly two-thirds of Indians surveyed in a recent poll commissioned by The Times of India said Hindu nationalist groups allied with the Bharatiya Janata Party, or B.J.P., were hurting “the development agenda.” Earlier this week, an upstart political party trounced Mr. Modi’s B.J.P. in local elections in the territory of Delhi. Last year, his party swept all seven races for the lower house of Parliament in Delhi.

Economic euphoria can evaporate quickly. When I lived there in 2010, the Indian economy roared back to life after the financial crisis, and seemingly everyone thought the good times were back for good. The Economist magazine, for example, published on its cover a photo of a racing tiger under the headline “How India’s growth will outpace China’s.” But that growth spurt fizzled largely because political leaders at the time became complacent and let corruption and mismanagement spiral out of control.

Later this month, Mr. Modi’s government is scheduled to present its first full-year budget. Investors and business executives are hoping that it will include proposals for transportation projects, the sale of government-owned companies and changes in taxation. While such measures are important, the budget will have failed if it does not offer a plan to improve public services like education, health and housing.

Mr. Modi cannot be expected to cure all of India’s problems. For one thing, he is not as powerful as he seems. Like the United States, India is a federal country in which state governments provide most public services. His job is to use all the tools at his disposal to make sure the poorest Indians are not left behind as the economy revs up.