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Should the federal government bail out some companies experiencing financial stress and possible bankruptcy while letting other companies go under?

Should the federal government bail out some companies experiencing financial stress and possible bankruptcy while letting other companies go under?

During the 2007-2009 recession, the Federal Reserve Bank loaned $85 billion to AIG to prevent the large insurance company from filing for bankruptcy. Lehman Brothers filed for bankruptcy during the same week and did not receive any government assistance. The Federal government also insured loans to General Motors and Chrysler.
In July, 2008, 5644 companies went bankrupt in the United States. That represented an 80% increase from the previous year.
Should the federal government bail out some companies experiencing financial stress and possible bankruptcy while letting other companies go under?

How do each of the following relate to the financial crisis of 2007-2008: declines in real estate values, sub-prime mortgage loans, mortgage backed securities, AIG?