Question

what did john maynard keynes believe should be the governments role in the economy?

Answer 1

Here's a quick quote out of one of the books that I have that I believe answers your question:

"Keynesian Theory
Keynesian economics advocates the use of direct government intervention as a means of achieving economic growth and stability. British Economist John Maynard Keynes offered an alternative to the view that the economy worked best when left to its own devices.
Example: Consider the case when the economy enters a recession. Keynesians advocate an increase in government spending or lower taxes to raise consumer income. With more money in their pockets, consumers increase their spending on goods and services. To meet the higher consumer demand for their products, businesses hire more workers to expand production and unemployment falls. Lower unemployment leads to a further increase in consumer income and spending. The increase in income and spending may continue for some time. However, once policymakers believe that spending is rising too quickly, policy will change to reflect lower government spending and higher taxes.
The analysis Keynes put forward became the rationale for the use of government spending and taxation to stabilize the business cycle.
When spending was insufficient and a recession loomed, government would pursue a policy of increased spending and lower taxes. During an economic boom and when higher spending threatened inflation, government policy would change in favour of lower spending and higher taxes."
-source: Canadian securities course