MOSCOW — Even as Russia has muscled back onto the world stage politically, its economy suffers from flat growth and shrinking incomes.

President Vladimir V. Putin has a plan to change that — and it involves pianos.

Kremlin officials say they will use an important investor conference opening Thursday in St. Petersburg to promote a new, six-year $400 billion stimulus plan, covering a dozen sectors of the economy. There are some classic big-spending efforts, like building roads and airports. And then the plan gets creative.

It calls for Russia to buy 900 pianos and build 50 covered ice rinks. Russian scientists will, by 2024, publish 200 articles on genetics in top-rated journals, the plan states.

Critics are calling it a step backward that would expand the state’s role in economic decisions, down to the level of purchases by classical music schools. They likened it to Gosplan, the planned economic model of the Soviet era, and it comes a few months after businessmen in Russia were told to rally behind the state and increase capital investments. It is also another effort by Russia to work around American and European sanctions.