Women in the late 1800's still could not vote.
Deciding how to spend the money coming from the tax collection is the main function of the government. Government must have to decide where they would invest the tax money in order to control the inflation and also to increase the productivity of its their country.
"... the chief business of the American people is business." he once said.
Coolidge followed a laissez-faire economic policy, whereby the government doesn't interfere in the national economy unless absolutely necessary, and even then its actions should be limited to gentle nudges to get the economy back on track rather than large scale intervention.
So, Coolidge's attitude toward business was 'if it's not broken, don't fix it' - leave business alone to prosper.
Answer: Reduce size and spending
