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. It is socially optimal for Fatlandia to 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.  It is socially optimal for Fatlandia to have:

Quizplus · Accepted Answer

The socially optimal number of army bases is where the marginal benefit equals the marginal cost. Looking at the table, we can see that the marginal benefit of the first army base is $12 million, the marginal benefit of the second army base is $10 million, and the marginal benefit of the third army base is $7 million. The marginal cost of each army base is $8 million. Therefore, the socially optimal number of army bases is two, where the marginal benefit of the second army base ($10 million) equals the marginal cost of an army base ($8 million). Hence, the answer is B.

There Are Ten States in the Democratic Nation of Fatlandia