When to use the market and when to use central planning? I have a basic question: my understanding is that in a market economy, economic decisions are governed by prices, i.e prices signal what should be produced &amp; how much. This is opposed to central planning, where a committee decided what should be produced &amp; how much. 

Now, in companies or households, such economic decisions are made by "central planning": i.e. - the CEO/board, or parents. Why shouldn't prices be used at these levels too? For example, why don't companies create a "currency" and tell employees to work on things that people with more "money" (senior management) will buy? Or, in a family, for parents to create a "currency" and tell family members to work on things that others will pay for? (done in small ways in some families, but not with everyone participating).

Bottom line of the question: When is it better to use a "market economy" (with prices) as compared to central planning? Is it a function of size? I don't think so...
There is a school of thought that says that people unconsciously use cost-benefit analyses in their relationships with other people. In this idea, people show kindness only because they anticipate getting rewarded for those acts, so it is in their own self-interest to do so. 

Monetizing small tasks takes time, and then collecting money for tasks done takes more time. So people do this mentally instead, moreso by feelings than rational calculation. At the level of an interpersonal relationship, words and feelings matter whereas in a business relationship, only tasks and services or goods rendered matter. Thus, monetizing the countless miniscule interactions that take place in a personal relationship would be impossible and there needs to be some degree of trust to replace that. 

At the level of a firm, an employment contract stipulates generally what somebody is being paid for. It is more efficient for the company to let individuals decide what to do in a day, or to instruct them to undertake certain tasks (depending on the organizational structure of the firm) than to spend time haggling for a price at which they should be paid in order to carry out various parts of their jobs. As other users have commented, when a firm gets too large, there are diseconomies of scale as it becomes too difficult to control a large number of workers. Then work tends to be contracted out to other firms and the use of money comes in.

However, token economies work well in situations such as mental asylums, to encourage those people to undertake tasks and follow rules.