Answer:
Productivy would go up only as long as some of the workers can become competent managers.
Step-by-step explanation:
The problem with worker ownership of the means of production (the firm), which is what socialism is about, is that workers do not necessarily have managerial skill, and as result, are likely to be unable to run the company efficiently.
In case this does not happen, and the workers manage to run the company well, GDP would increase because productivity in the firm would rise. Inflation would likely fall down because more productivity means more output of goods and services, and inflation tends to have a inverse relationship with output (although it also depends on other variables like the rate of growth of the money supply).
Finally, another macroeconomic variable that would positively affected is employment rate, because a more efficient company would likely require new workers.