Reducing pipe size on Booster pump
You can reduce the output size with few problems except limiting the flow, pushing into a pressure tank will be better on the pump unless a variable frequency drive is used. Limiting the input can cause severe cavitation and damage the impeller and housing in a short period of time.

Normally a smaller size pump will cost less and have smaller ports, even using a 1/2” pump may have issues if your draw is larger than the supply this can cause a neighbors faucet when opened to suck air in. 

In my area for systems that can not provide enough water we usually install a large tank like 500 gallons and put the booster on the out put of that tank, a simple float valve at the top of the tank stops the incoming water when the tank is full just like a toilet tank valve. I was thinking of a ball on a lever not a modern fluid master.

Size the tank based on several hours or daily water usage.