When policy makers in Washington worry about Mexico these days, they think in terms of a handful of numbers: Mexico’s 19,500 hectares devoted to poppy cultivation for heroin; its 17,500 hectares growing cannabis; the 95 percent of American cocaine imports brought by Mexican cartels through Mexico and Central America.They are thinking about the wrong numbers. If there is one number that embodies the seemingly intractable challenge imposed by the illegal drug trade on the relationship between the United States and Mexico, it is $177.26. That is the retail price, according to Drug Enforcement Administration data, of one gram of pure cocaine from your typical local pusher. That is 74 percent cheaper than it was 30 years ago.This number contains pretty much all you need to evaluate the Mexican and American governments’ “war” to eradicate illegal drugs from the streets of the United States. They would do well to heed its message. What it says is that the struggle on which they have spent billions of dollars and lost tens of thousands of lives over the last four decades has failed.There is little reason to expect the elections this year will do much to address the challenges to the bilateral relationship. Enrique Peña Nieto, elected president of Mexico on Sunday, is a scion of Mexico’s Institutional Revolutionary Party, which was tainted by authoritarianism, corruption and fraud during seven decades in power, before it was booted out by voters 12 years ago. In the United States, neither President Obama nor his Republican challenger, Mitt Romney, has shown much interest in the nation’s southern neighbor.Yet the presidential elections on both sides of the border offer a unique opportunity to re-examine the central flaws of the two countries’ strategy against illegal narcotics. Its threadbare victories — a drug seizure here, a captured kingpin there — pale against its cost in blood and treasure. And its collateral damage, measured in terms of social harm, has become too intense to ignore.Most important, conceived to eradicate the illegal drug market, the war on drugs cannot be won. Once they understand this, the Mexican and American governments may consider refocusing their strategies to take aim at what really matters: the health and security of their citizens, communities and nations.Prices match supply with demand. If the supply of an illicit drug were to fall, say because the Drug Enforcement Administration stopped it from reaching the nation’s shores, we should expect its price to go up.That is not what happened with cocaine. Despite billions spent on measures from spraying coca fields high in the Andes to jailing local dealers in Miami or Washington, a gram of cocaine cost about 16 percent less last year than it did in 2001. The drop is similar for heroin and methamphetamine. The only drug that has not experienced a significant fall in price is marijuana.And it’s not as if we’ve lost our taste for the stuff, either. About 40 percent of high school seniors admit to having taken some illegal drug in the last year — up from 30 percent two decades ago, according to the Monitoring the Future survey, financed by the National Institute on Drug Abuse.The use of hard drugs, meanwhile, has remained roughly stable over the last two decades, rising by a few percentage points in the 1990s and declining by a few percentage points over the last decade, with consumption patterns moving from one drug to another according to fashion and ease of purchase.For instance, 2.9 percent of high school seniors admit to having tried cocaine in the last year, just slightly less than in 1992. About 15 percent of seniors said they abused a prescription drug last year. Twenty years ago, prescription drug abuse was not even consistently measured.The only dimension along which the war on drugs might be conceived as a success is political. If you ask Americans how concerned they are about drugs, they will give you roughly the same answer they have given for years: not so much.In a Gallup poll, only 31 percent of Americans said they thought the government was making much progress dealing with illegal drugs, the lowest share since 1997. But fewer people say they worry about drug abuse than 10 years ago. Only 29 percent of Americans think it is an extremely or very serious problem where they live, the lowest share in the last decade.But the government has spent $20 billion to $25 billion a year on counternarcotics efforts over the last decade. That is a pretty high price tag for political cover, to stop drugs from becoming a prominent issue on voters’ radar screen. It becomes unacceptably high if you add in the real costs of the drug wars. That includes more than 55,000 Mexicans and tens of thousands of Central Americans killed by drug-fueled violence since Mexico’s departing president, Felipe Calderón, declared war six years ago against the traffickers ferrying drugs across the border.And the domestic costs are enormous, too. Almost one in five inmates in state prisons and half of those in federal prisons are serving time for drug offenses. In 2010, 1.64 million people were arrested for drug violations. Four out of five arrests were for possession. Nearly half were for possession of often-tiny amounts of marijuana.Harry Levine, a sociologist at Queens College of the City University of New York, told me that processing each of the roughly 85,000 arrests for drug misdemeanors in New York City last year cost the city $1,500 to $2,000. And that is just the cost to the budget. Hundreds of thousands of Americans, mostly black and poor, are unable to get a job, a credit card or even an apartment to rent because of the lasting stigma of a criminal record for carrying an ounce of marijuana.Cracking down hard on drug users may sound great on the stump. But Americans who inject drugs are four times as likely to have H.I.V. as British addicts and seven times as likely as drug-injecting Swiss, mainly because the United States has been much slower in introducing needle exchanges and other measures to address the impact of drug abuse on public health.The Obama administration acknowledges the limitations of the drug wars, and has shifted its priorities, focusing more on drug abuse prevention and treatment of addicts, and less on enforcement.Still, many critics of the current policy believe the solution is to legalize — to bring illegal drugs out of the shadows where they are controlled by criminal gangs, into the light of the legal market where they can be regulated and taxed by the government.Jeffrey Miron, an economist at Harvard who studies drug policy closely, has suggested that legalizing all illicit drugs would produce net benefits to the United States of some $65 billion a year, mostly by cutting public spending on enforcement as well as through reduced crime and corruption.A study by analysts at the RAND Corporation, a California research organization, suggested that if marijuana were legalized in California and the drug spilled from there to other states, Mexican drug cartels would lose about a fifth of their annual income of some $6.5 billion from illegal exports to the United States.A growing array of Latin American presidents have asked for the United States to consider legalizing some drugs, like marijuana. Even Mr. Calderón is realizing the futility of the war against the narco-syndicates. He asked President Obama and the United States Congress last month to consider “market solutions” to reduce the cash flow to criminal groups.Legalization may carry risks, too. Peter H. Reuter, one of the authors of the RAND study, who is now a professor of public policy in the department of criminology of the University of Maryland, said he worried that legalizing drugs would vastly expand drug abuse, leading to other potential social and health costs. Supporters of the war on drugs insist that without it, consumption would have soared to the heights of the 1980s and perhaps beyond.There are other options. The Global Commission on Drug Policy, whose membership includes former presidents of Mexico, Colombia, Chile, Brazil and Poland, has called on national governments to “depenalize” if not necessarily legalize drug possession and sales.This means stopping the arrest and imprisonment of people who use drugs but cause no harm to others, and going easy on small-scale dealers, whose arrest does nothing to dent the flow of illegal drugs. It means focusing enforcement efforts on reducing the violence of the drug trade, rather than eliminating the drug market itself. It may also entail giving drugs to the most addicted users, to get them into clinics and off the streets.Such policies require a drastic change of approach in Mexico and the United States. Their governments could start by acknowledging that drug dependence is a complex condition that is not solved through punishment, and that numbers of addicts or dealers arrested, or tons of drugs seized, are hardly measures of success.A war on drugs whose objective is to eradicate the drug market — to stop drugs from arriving in the United States and stop Americans from swallowing, smoking, inhaling or injecting them — is a war that cannot be won. What we care about is the harm that drugs, drug trafficking and drug policy do to individuals, society and even national security. Reducing this harm is a goal worth fighting for.