What problems will economists have to solve in the next 20 years?
As many observers have noted, economists are not especially good at forecasting the future. Nonetheless, intellectual trends generally move slowly. So I would expect that the issues economists deal with in the next twenty years will look a lot like those that have occupied them in the last twenty years.
To be more specific, economists will continue to work on ways to: integrate insights from psychology to develop more realistic models of individual decision-making, better identify causal relationships in the economy, and more precisely forecast the impacts of fiscal and monetary policy tools on the aggregate economy.
The tools of economics can be applied to many issues in public policy and business strategy. I would expect that issues related to climate change, slowing population growth and the impacts of economic dis-integration (e.g., Brexit) will be among the issues with which economists concern themselves. Other important topics will include the growing economic importance of the online economy, the impacts of social media, inequality, and the effects of automation on work and workers.