Question

This question is about the economics of the military draft. Urbana is a country in Eastern Europe with 5000 citizens. The government wishes to recruit an army. The supply of labor to the armed forces is given by

Qs = -100 + 20W

a. Graph the supply curve.

b. Suppose the government wishes to recruit an army 200. What wage will it have to pay workers to recruit an army of this size?

c. The government decides that it is too expensive to have the all volunteer army in b.   Suppose the government sets a wage of 10. At this wage, some workers will volunteer for the army. It then will draft by random lottery enough citizens to reach the required army of 200. It will pay these draftees 10. How citizens will they have to draft? Explain your answer.

d. Suppose the government allows each person drafted the option of paying a worker to takes their place in the army. How much will you have to pay somebody to join the army in your place?

e. Which system is best in terms of economic efficiency? Justify your answer.

Answer 1

Answer: Population of the Urbana country = 5000 citizens

Supply function Q_S = -100 + 20 W ---------------------------------(1)

a). Graph the supply curve:

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b).   Quantity Demanded = 200;

We need the supply of 200 people in this case, so putting the value of Q = 200, in equation (1)

Q_S = -100 + 20 W

200 = -100 + 20 W

20 W = 300

W= 15

Hence to recruit 200 people in the army, Government need to set the Wage at 15 units.

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c). Government set the Wage W = 10

At this wage the citizens which will come voluntarily :

Q_S = -100 + 20 * 10

Q_S = 100

100 people will come voluntarily and rest (200 - 100 =100), government will have to draft for random lottery.

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d). If government allows each person drafted the option of paying a worker to take their place in the army:

The replaced person will not join at a wage of 10; as all 100 people who were willing to join army at wage 10 have already taken the place. The other 100 can join only if they get some added amount apart from wages.

So to replace for each member, the selected member will have to pay 5 units extra to get one person who can replace him. As with the wage =15, there will be more people who will join the army voluntarily.

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e). The draft system is more efficient economically. As all the resources who will join will be on their preference and there will be no consumer or producer surplus.

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