Formal pairs suit Writing Task 2. Neutral ones work anywhere. Informal ones belong in Speaking.
1.allocate public funds
formalofficially decide how government money is spent
Governments must decide how to allocate public funds between health, education and defence.
Allocate resources and allocate a budget follow the same pattern.
2.cut public spending
neutralreduce the money a government spends on services
When governments cut public spending, the poorest families are usually hit hardest.
Reduce is more formal; slash is more dramatic and journalistic.
3.raise taxes
neutralincrease the amount of tax people pay
Few politicians are willing to raise taxes before an election.
Raise takes an object; rise does not.
Avoid: rise taxes → raise taxes
4.implement a policy
formalput a planned course of action into effect
It is easier to announce a reform than to implement a policy successfully.
Introduce and adopt also collocate with policy.
5.introduce legislation
formalbring in new laws
The government plans to introduce legislation banning sugary drinks in schools.
Pass a law is the more neutral equivalent.
6.the welfare state
formala system in which the government pays for health care, pensions and support
The welfare state protects people who lose their jobs or fall ill.
Always with the in this sense.
7.social inequality
formalunfair differences in wealth and opportunity between groups
Free school meals are one way to reduce social inequality.
Reduce, address and widen collocate with it.
8.the gap between rich and poor
neutralthe difference in wealth between wealthy and poor people
The gap between rich and poor has widened in many countries.
Widen and narrow are the natural verbs.
9.an ageing population
formala population with a growing share of older people
An ageing population means fewer workers paying for more pensions.
British spelling: ageing.
10.provide public services
neutralsupply services such as hospitals, schools and transport
Local councils provide public services with money from national government.
Fund and deliver also collocate with services.
11.bear the cost of
formalpay for something, often unwillingly
Taxpayers ultimately bear the cost of failed infrastructure projects.
Bear the burden and bear responsibility follow the same pattern.
12.play a key role in
neutralbe very important in a process or result
Charities play a key role in supporting homeless people.
Use in before the activity.
Avoid: play a key role for → play a key role in
13.the general public
neutralordinary people rather than experts or officials
Scientific reports are often too technical for the general public.
Always with the.
14.exercise the right to vote
formaluse your legal right to vote
Fewer young people exercise their right to vote than older citizens.
Exercise collocates with rights; use is less natural here.
15.invest in infrastructure
formalspend money on roads, railways, power and water systems
Countries that invest in infrastructure tend to attract more foreign business.
Infrastructure is uncountable: no -s.