There are ten states in the democratic nation of Fatlandia, and each state has ten thousand residents. Although incomes vary, each Fatlandian pays a tax equal to the total cost of all government projects divided by the number of residents in the country. Currently, two states each have one army base. An army base adds $2 million to a state's local economy each year. In addition, in terms of increased security, the annual marginal benefit to Fatlandia of having an additional army base is shown below. The total cost of an army base is $8 million per year. If Fatlandia builds a third army base, the country will have:

Question

There are ten states in the democratic nation of Fatlandia, and each state has ten thousand residents. Although incomes vary, each Fatlandian pays a tax equal to the total cost of all government projects divided by the number of residents in the country. Currently, two states each have one army base. An army base adds $2 million to a state's local economy each year. In addition, in terms of increased security, the annual marginal benefit to Fatlandia of having an additional army base is shown below. The total cost of an army base is $8 million per year.  If Fatlandia builds a third army base, the country will have:

Quizplus · Accepted Answer

The efficient number of army bases is the point where marginal cost (MC) equals marginal benefit (MB). From the given table, we can see that with two army bases, the marginal benefit is $1.5 million per year. If a third army base is built, the marginal benefit will decrease to $0.5 million per year.

The marginal cost of building an additional army base is $8 million per year. Thus, the efficient number of bases is two, as the marginal benefit of the third base ($0.5 million) is less than the marginal cost ($8 million).

If a third army base is built, Fatlandia will have more than the efficient number of bases, leading to a net loss of $7.5 million per year ($8 million marginal cost - $0.5 million marginal benefit). Therefore, the best choice is not to build a third army base.

There Are Ten States in the Democratic Nation of Fatlandia