  Borrowing ideas from {\em Production functions} in micro-economics, in this
paper we introduce a framework to systematically evaluate the performance and
cost trade-offs between machine-translated and manually-created labelled data
for task-specific fine-tuning of massively multilingual language models. We
illustrate the effectiveness of our framework through a case-study on the
TyDIQA-GoldP dataset. One of the interesting conclusions of the study is that
if the cost of machine translation is greater than zero, the optimal
performance at least cost is always achieved with at least some or only
manually-created data. To our knowledge, this is the first attempt towards
extending the concept of production functions to study data collection
strategies for training multilingual models, and can serve as a valuable tool
for other similar cost vs data trade-offs in NLP.
