There's a difference between the market economy, the political economy
and the overall economy in that the market economy and the political economy
are subsets of the overall economy. This mix differs fro country to country.
For example in Australia Governmants (Comm + States & Munis) share of
GDP was just under 30% with the remaining 70% being private enterprise:

(source ABS)
While Governments' taxation and spending impacts the private economy,
it is foolhardy to say that the Government manages the economy; it manages
the political economy.
But politicians , especially Treasurers , think that the tail can wag the dog!