To take advantage of the division of labor, production was organized in large factories. People became wage workers they sold the services of their labor to the owners of the factories and were paid wages. Resource allocation refers to the distribution of the factors of production among their alternative uses. In a market economy consumers decide what to buy and in what quantities given the prices that prevail in markets, and producers decide what to produce and in what quantities given the prices that prevail in markets. Resource allocation is determined by all of these independent decisions made through the medium of markets.
Households are the ultimate consumers of goods and services.
Firms are the producers of capital and final goods and services. There is no assumption that government behaves in a consistent manner. Some models assume personal interests motivate elected officials. The distinction is a legal one whether the firms are owned privately or by the government. Institutions are formal and informal ways of organizing human behavior.