The government of country is thinking of forming an army. For simplicity, assume

Question

The government of country 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? Is there any deadweight loss of forming the army through this mechanism? If so, calculate the 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 deadweight loss? If so, explain why, and calculate its value.

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 deadweight loss? If so, calculate its value.

Explanation / Answer

a. the army will be in the size of maximum 200 and minimum 100

b. around 160 people will join into the army if the wage is $160, above this is the deadweight of customer and below this point is dead weight loss of army

c. yes there is deadweight loss at this levels.

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