In modern societies, the traditional market is not a viable answer to the economic problem. It was long ago that people as a matter of course followed in their family's footsteps regarding what to make and how to make it; how to allot the scarcity of resources (land, labor, capital, and management). The conundrum for modern society is that once depression or recession or inflation take hold, the market economy approach can't sustain the economy unaided either. Here enter the noble concept mentioned by rrteacher of "just prices."
One tradition that is collapsing is that of charitable giving. Many people -- myself included -- are unable to justify any out-of-pocket charity because we have little enough to live on ourselves. Taxes, prices, inflation, and falling incomes are causing people to resent the government taking their money and spending it without their -- or any -- oversight. As government expands its purview over private citizens, we become unable to give for moral (or religious) reasons because we simply cannot afford it.
Tradition in many ways as #3 establishes is a force that does seem to offer easy and accessible answers to the economic problem, but these are also answers that will not, in the long term, solve the economic problem and guarantee long term success and growth. Tradition by its very definition does not encourage the kind of innovative thinking that is necessary for any company or family to succeed in the business world, as it does not encourage you to think out of the box. Any answer given to the economic problem by tradition will therefore be very limited.
Post #3 clearly answered the question in the way the original post wanted, and it reminded me of another aspect of a traditional, or pre-modern economy that seems lost today. In times of economic hardship, people reverted back to what has often been called a "moral economy" based on "just prices" rather than market prices. What many accept today as dogma- the idea that the market should dictate the price of goods and services even if it means many people can't afford the most basic items, is a pretty new innovation.
The "economic problem" also deals with having enough resources for everyone. Although the United States works diligently at trying to provide enough goods and services for everyone, it is apparent that it is not working. In the last couple of years, the percentage of people living in poverty has increased to approximately 15% and there are over 46 million people on food stamps. Is there not enough goods and services, or are they not reaching the people? Tradition will only get us so far, but will not solve the "economic problem" facing the United States.
I do not believe that the first answer is really what the questioner is looking for.
In economics, the "economic problem" is defined as the problem of deciding what to make, how to make it, and who to make it for. You can see this in any economics book, for example, here.
A traditional economy is one of the three types of economy (traditional, market, command). In a traditional economy, the questions that make up the economic problem are answered by tradition. What will we make? We will make whatever our parents made. If our parents farmed, we will farm. How will we make it? Again, however our parents did. We will not try to innovate. We will just do things as they have always been done. For whom will we make it? Again, tradition. We will probably make it for ourselves. If it is traditional, we will give some to the village elders or the chief. We might give some away to relatives. We will not be driven by concerns about profit or anything like that.
So, in terms of economics, this is how tradition answers "the economic problem."
This is great question. It is probably good to start off with a simple premise that many people in economics agree with. This is the notion that there are cycles in the economy. If this is true, then tradition or history can be a great teacher about how to solve problems. This is why there is an adage out there, which states: "Those who do not know history are destined to repeat it."
From this perspective, knowing the history of bad economic times can help tremendously in planning an economic recovery. Chairman Ben Bernanke is doing exactly this. Before he became the chairman of the Federal Reserve, he was an academic historian of the Great Depression. Based on his knowledge of the Great Depression, he is trying to make policies that will help the United States to overcome their economic hardships. He is trying to pump money into the system, so that people will borrow and spend with the hopes of reviving the economy.