Shabbily dressed women, holding hungry, crying infants, beg for a few pesos in front of shops offering the latest in expensive fashions. On every street corner men, women and children hawk newspapers and lottery tickets.

The scene is Mexico City, a sprawling megalopolis that will be the largest city in the Western World in 10 years. Its frequent fogs enshroud the richest of the rich and the poorest of the poor in a land of contrasts, about which most Americans are woefully ignorant.

Our associate Jack Mitchell has been to Mexico City to explore the reasons that relations between the United States and Mexico have taken a turn for the worse in recent years. Basically, what he found out was that the Mexicans, aware of the international importance of their new status as an oil-rich nation, will no longer put up with the patronizing, Big Brother attitude of the United States. The insatiable U.S. thirst for oil has given the Mexicans new bargaining power.

Mexico's economic and social problems are staggering. The unemployment rate tops 20 percent. An equal number of Mexicans are underemployed, forced to scramble for a meager existence with a variety of odd jobs. Half the country's population of 67 million is under 18, and as many as 100,000 children die each year from malnutrition. The overpopulation will grow worse in the next few years: there will be more than 100 million Mexicans by the year 2000, according to current estimates.

But Mexico's future is not totally bleak. Despite the widespread poverty and unemployment, the country's political and economic systems remain remarkably stable. The days of military coups are apparently gone forever. And the discovery of vast oil and natural gas reserves -- on a scale with Saudi Arabia's -- has made Mexico's long-range economic picture brighter.

The real problem is not Mexico's lack of wealth, but the inequitable distribution of its natural resources. The wealthiest 10 percent of the population takes 45 percent of the national income, while the 40 percent of the population at the lowest end of the scale must make do with 10 percent of the income. The rest of the citizenry exists with little hope of rising into the wealthy class -- but with an ever present fear of slipping into the ranks of the poor.

Yet even the poorest have heard of the oil riches and have at least a dim awareness that life should improve as a result. The rising expectations and growing self-respect of ordinary Mexicans could lead to chaos if the government's ambitious social programs -- to be financed largely by oil revenues -- prove to be no more successful than the failed land and agricultural reforms of the past.

The man charged with preventing such a catastrophe is President Jose Lopez Portillo. A balding, athletic man -- he jogs and throws the javelin -- Lopez Portillo mirrors the people he governs: "Pepe," as he likes to be called, is informal, energetic, impatient for the future and imbued with a confidence in his country's role in the Western Hemisphere.

His relations with Jimmy Carter have been less than chummy. In belated recognition of their two countries' sharply changed relationship, Carter caved in on the Mexican's price demands for a natural gas deal, ending two years of bitterness touched off by former energy label of a big-spending liberal, before he has time to move to the Carter is trying to be more diplomatic about the continuing problem of illegal aliens entering the United States from Mexico.

But Carter's choice of representatives has done little to convince the sensitive Mexicans that the old days of overbearing "dollar diplomacy" are gone. Ambassador Patrick Lucey, who speaks little Spanish, put his foot in his mouth over the sensitive gas negotiations. Former Texas congressman Robert Krueger created at least one unfortunate incident in his role as ambassador-at-large to Mexico, promoting a few senators to ask at his confirmation hearing if his appointment was really necessary.

What the Mexicans want, quite simply, is to be treated as equals. If U.S. policymakers fail to grasp this point, the Mexicans will retaliate with their new economic weapon: oil. They understandably fail to see why they're not entitled to as much respect as the Arab oil sheiks.