Also, in a free market farmers would have a reason to invest money to get higher crop yields. Fertilizer, pesticides, better seed, and sometimes irrigation equipment can increase the production from the same plot of land by several times - but they cost money that cannot be recovered if the price of food is artificially low. In addition, low food prices may cause farmers to switch to exportable non-food crops that pay more, like cotton, coffee, or opium.

This doesn't necessarily mean that just establishing a free market will save a third world country from starvation. There may not be money available for even beginning to make these investments. Farmers have to learn about how such improvements are possible in the first place. Transportation is often a severe limiting factor. Since most third-world major cities are seaports or on navigable rivers, it's often cheaper to grow wheat in Minnesota and ship it by rail and sea to a foreign city than for farmers in that country to send wheat 100 miles overland to the city over dirt trails. This doesn't leave them much reason to develop agriculture beyond the subsistence level (aside from certain crops with a high enough value per pound that it's worthwhile to carry them to market on your back-but these crops are hardly ever edible, and mostly are illegal). Finally, if the farmers don't have the transportation to ship food crops to market, then when crops fail, there is no transportation to ship imported food from the city to the countryside and the farmers starve.

This lack of a basic transportation infrastructure is another example of how governments misallocate resources, especially under political systems that elevate the government above the people. You can bet that when the local Glorious Leader goes out to see his mistress, his limo is riding smoothly on paved roads, but there's not much money left over for building roads to bring food to the market. This didn't happen so much in the USA because (at least in the beginning), it was understood that the government served the people and politicians that got too high and mighty would be back in the private sector after the next election - but still, the main way farm roads were constructed until the 20th century was by laws that required the farmers to turn out once a year and work on the roads themselves. In a socialist system, of course you can't let the people do things for themselves like this...

That and they have a dictator that steals what ever profit is made and forces his people into starvation.

Well put by all. The political system - dictator or free state - is the lynch pin of the problem. If the outside world believes that they can make a buck in a country, they will gladly lend money, expertise and equipment when a country hits hard times. But when you have some asswipe dictator stealing all of the potential profits, why take the risk?

And sending "humanitarian aid" only makes the problem worse because the dictator has no incentive to change his ways.

"In a market economy, prices will increase and suppliers will seek to fill the demand. If price controls are put into place, the lack of profitability means that many suppliers won't even bother."

In either case, poor people starve because they either cannot buy what is not there, or cannot afford to buy what is there.

Utopists seek to change this, but almost always the "solutions" they impose lead to greater death. Realists accept it, and understand that the implementation of free-market solutions results in very real, very tragic associated costs, but in the long run, fewer (but never zero) people suffer.