Notes

https://www.cliffsnotes.com/study-guides/sociology/economics-and-politics/politics-and-major-political-structure
https://www.intelligenteconomist.com/types-of-economies/

Traditional economic system: lack of technology and medicine; gives everyone a specific job and role in society; areas tend to be rural and are more tied to the land through farming.

Command: controlled by a centralized power; the core of the communist philosophy; government is usually the centralized power; able to create a healthy supply of resources with affordable prices; usually owns all significant industries like utilities, aviation, and railroad.
Advantages- a government can mobilize resources on a massive scale, provide jobs for almost all citizens, and can focus on the good for the society rather than the individuals.
Disadvantages- hard for central planners to provide for everyone's needs, meaning the government is forced to ration because it can't calculate demand since it sets prices, and lack of innovation since the people in the population are forced to pursue jobs the government deems fit.

(Free) Market: firms and households act in self-interest to determine how the economy works; the opposite of command economy, where the central government gets to keep the profits; no government intervention in a pure market economy, however, it doesn't exist in this world; capitalist nations' government regulates (attempts to control) fair trade, government programs, honest business, monopolies, etc; separation of government and economy (which prevents the government from becoming too powerful and keeps interests aligned with the markets').
Advantages- consumers pay the highest price they want; businesses only produce profitable goods and services; lots of inventive for entrepreneurship; efficient use of the factors of production because businesses are very competitive; businesses invest in research and development; constant innovation as companies compete to provide better for consumers.
Disadvantages- due to competition between businesses, they won't care about the disadvantaged (elderly or disabled, for example); higher income inequality; consumers can be exploited by monopolies; economic needs have priority over social and human needs, which combine with self-interest and isn't good.

Mixed: a cross between market and command; most commonly, the market is more or less free of government ownership (except for transport or defense and railroad); government is usually involved in the regulation of private businesses; the idea of this was to incorporate policies that are socialist and capitalist; most countries fall in this category.
Advantages- less government intervention than in command; private businesses can run more efficiently and cut costs that the government would; government would intervene to correct market failures (like break up large companies if they abuse monopoly power, or to reduce a negative externality of consumption); governments can create safety net programs (like healthcare or social security); they can also use taxation policies to redistribute income and reduce inequality.
Disadvantages- there is always a dispute over whether or not the government is intervening too much or too little; state-run industries are often subsidized by governments and run into debts by being uncompetitive.