An economy in which a central authority draws up a plan that establishes what will be produced and when, sets production goals, and makes rules for distribution is a a. laissez-faire economy. b. command economy. c. public-goods economy. d. free-market economy.

A laissez-faire economy is one where there is no interference within the government, so that's not correct.

There's no such thing as a public-goods economy (according to google at least), but public goods are things that the government provides for the most part. It's accessible by everyone.

A free-market economy is where the government has little to no control, similar to a laissez-faire economy, so that's not right.

Your question is literally the definition of a command economy, so that's right!

Owners, investors and venture capitalists want to recoup their money .

True, it has more income then it spends.