Consider two individuals, Jay and Randy, and their decision to serve in the military. The accompanying tables show their opportunity costs of supplying military service. The government has determined that it needs 12 total hours of military service per week from these two individuals.
(i) Suppose the government drafts Jay and Randy, requiring each individual to serve 6 hours per week and paying them $15 per hour. What is society's cost of the 12 hours of military service?
(ii) What is the least possible cost to society of having 12 hours served per week?
(iii) What policy could the government use to obtain the required 12 hours of military service at the least possible cost to society?
(i) The cost to society of military service is the sum of the opportunity costs of its soldiers and is independent of the wages paid to those soldiers. Jay's opportunity cost of supplying 6 hours of service is $42, and Randy's opportunity cost is $126. The cost to society of 12 hours of military service is thus $168.
(ii) For the cost to be as small as possible, Jay and Randy should have equal marginal costs. Jay should supply 9 hours of service per week (with an opportunity cost of $90), and Randy should supply 3 hours of service per week (with an opportunity cost of $36). The least possible cost to society is thus $126.
(iii) If the government offers to pay $18 per hour in a volunteer system, then Jay and Randy will choose to supply 9 and 3 hours per week, respectively, and the cost to society will be as small as possible.
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