What Do Computers Do to Productivity?

It was said to me that the computers virtually don't increase the productivity. Is it true?

Also a subquestion: what is the "productivity" in IT sector? When you use your program and one anoyther customer downloads your program, will your productivity increase twice?

Is there a way how to measure productivity of IT sector?

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Let's start at the last question. What is productivity? Productivity (regardless of the industry) is value added per worker. Value added is the sum of wages (broadly defined, including benefits) and profits. In other words, productivity is how much money a worker makes for herself plus how much money she makes for her employer. So in your example, there is simply not enough data to even begin to reason about productivity.

Productivity, however, is not the whole story. Sometimes, productivity can actually decrease because of the gains made by the consumer. Say, certain industry employs 1,000 workers, sells 1,000,000 widgets a year for $100 each and pays workers $40,000 a year on average. Cost of materials is $30 per widget. So value added by this industry is 1,000,000 * ($100 - $30) = $70,000,000, including $40,000,000 in wages and $30,000,000 in profits; productivity, thus, is $70,000,000 / 1,000 = $70,000. Now, let's say that the industry made some productivity gains in physical terms and now sells 1,100,000 widgets a year without any increase in labor employed, but prices dropped to $80 due to competitive pressures. So value added by the industry is now 1,100,000 * ($80 - $30) = $55,000,000, including $40,000,000 in wages and $15,000,000 in profits; productivity, thus, is $55,000,000 / 1,000 = $55,000. Note that although labor became more productive in physical terms, the productivity measured in monetary terms actually decreased; income to labor (wages) didn't change, income to capital (profits) decreased, but the consumer surplus increased (consumes got more widgets at lower prices).