What are some of the ways in which the government is involved in the economy? what are the advantages and disadvantages of governmental involvement?

The government can control tariffs and can limit how much can be imported into the usa.
The government can provide subsidies to certain producers, typically farmers.
The government can put a ceiling and a floor on prices as they wish. They can control the lowest and highest price a commodity can sell for.
The government can own public works such as a water company if they feel they can provide the service for a lower cost than the local competitors.
The government can decide which companies are monopolies and which companies are violating federal policies regarding trade. The government has the power to break up monopolies.
Each of these has advantages and disadvantages. For example, for farmers, when prices on their crops are too low, the government "gives" them money for their crops so they can stay in business.
A monopoly business controls the price and supply. If the monopoly is broken up, then competitors can enter the field- this can help drive down prices.
If the government can provide utility services for cheaper, that is good.

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