Question

As a result of losing a major war, Country A was forbidden to have an army. However, world circumstances have changed and country A has become an important economic power. Other countries now want country A to take a more active role in preserving the prevailing world order. The government of country A is thinking of forming an army. For simplicity, assume that country A has 100 citizens. The opportunity cost for each citizen of joining the army varies from $101 to $200. Assume that citizens are ordered in an ascending way according to their opportunity cost of joining the army (i.e., person number 35 has an opportunity cost of $135 of joining the army). The value to society of having a person in the army is $160.

a) What is the optimal size of the army? Use a graph showing the demand and supply for army personnel to support your answer.
b) How many people will join the army if the government offers a wage of $160? Who will those people be? What is the net benefit for the country of having this army? (HINT: consider the value to society from each individual that joins the army and the benefits that each individual gains from joining the army) Is there any dead weight loss of forming the army through this mechanism? If so, calculate the monetary value.
c) What happens if the government drafts the optimal number of persons at random (assume the pay continues to be $160)? Is there any dead weight loss? If so, explain why, and calculate its monetary value. (HINT: consider the average opportunity cost for someone who is drafted and compare this new equilibrium with the case without government drafts). d) What happens if the government drafts the optimal number of persons at random but now allows individuals to pay someone else to take his/her place. Is there any dead weight loss? If so, calculate its monetary value.

Answer 1