The classical economists had beliefs about wealth and value that differed somewhat from the beliefs we hold today. Economists like Adam Smith and David Ricardo believed that value was as much a product of labor costs as supply and demand, and that there was an "intrinsic value" to goods distinct from the value of those goods in the market. Ricardo, in particular, argued that there were two forms of value: value from the cost of land and labor, and value resulting from scarcity.
Adam Smith developed a view of human nature that continues to influence economic thought to this day. According to Smith, human nature is guided by self interest. People seek naturally to increase their wealth, and engage in business for the purpose of maximizing ultility. When people maximize their wealth by fair exchanges of value, argued Smith, the "invisible hand" of the free market produces economic benefits for everyone in society.
Classical economists believed that the market should be left free and (mostly) unregulated. Adam Smith, for example, argued that the free market was in sync with human nature, and that a free market allowed for the operation of "natural forces" that lead to creation of wealth. Ricardo argued that unrestricted trade between nations leads to the creation of wealth for each partner. Mill believed that human welfare would be maximized if people were free to make their own choices, in the market and elsewhere.
Rent was a topic of particular interest to the classical economists. Smith believed that rent was an effect of prices; that is to say the rent paid on a piece of property was a consequence of the prices of all goods and services that could be produced from that land. Smith and Ricardo both felt that landlords created economic inefficiencies, as they charged money for the use of resources they themselves did not create or contribute to.
The classical theory of profit is very different from the neoclassical theory. The classical economists generally believed profit to be a kind of fee or salary paid to a working capitalist, similar to a wage paid to a worker. In this sense, the theory of wages and the theory of profits are highly interrelated in classical economics. However, Smith makes it clear that the two are not identical: one must own property to take a profit, while one must perform a service to demand a wage.