All voters in a city pay an equal marginal tax rate of $10 per mile of roads paved per year. The federal government has a matching grant program of road paving whereby 75 percent of the cost of road paving is paid.
Show how the matching grant affects the budget constraint for a typical voter. In equilibrium, the community receives $1 million per year for road paving under the matching grant program. Prove that the matching grant will be more effective in increasing road paving than a $1 million annual lump-sum grant.