Question

Reference: The Economics/Finance Section of the WSJ daily

Assume that voluntary enlistment into the U.S. Armed Forces does not ensure its full strength (i.e. ability to fight two wars simultaneously). Assume also that you are an economist who works for the U.S. Secretary of Defense. Your task is to determine a pay-raise in the (potential and existing) military personnel's salaries in order to ensure full strength of the U.S. Armed Forces. Furthermore, assume that the U.S. Armed Forces is forty percent (40%) short of its full strength and an empirical study found that own-price elasticity of supply coefficient for military service in U.S. is 2.25.

With the above information, by how many percent will the salary of military personnel in U.S. be raised so as to attract more potential enlistees (and retain the existing enlisted military personnel) and to ensure full strength of the U.S. Armed forces?

INSTRUCTIONS:

(1) Derive the answer to the (above) question Mathematically or Algebraically.

(2) Show all steps used in deriving your answer(s).

(3) Explain in detail, the economics of your derived answer.

(4) Use the appropriate steps and formula in deriving your answer(s).

(5) Discuss the weakness(es) or the shortcomings of using this type of technique in public policy practice.

Answer 1

We know that own price elasticity of supply = % change in supply offered / % change in price

Elasticity = 2.25

In this case, we also are told that the current shortfall is 40% and hence only 60% of positions are filled. In order for 100% of positions to be filled, we need to go from 60% to 100%, which is an increase of (100-60) / 60 = 66.67%

So, 2.25 = 66.67% / % change in price

Hence, % change in price = 66.67% / 2.25 = 29.63%.

What this means in terms of the budget of department of defense is as follows:

Assuming current spend on salaries = x

New spend with 100% positioned filled will be: 166.67% times 129.63% times x

166.67% is the headcount, and 129.63% is the average salary level, as % of today's

So the new spend would be 216% of current spend. This is more than doubling of current spend, which may or may not be feasible. Even if the budget is available in DOD, it may have a cascading impact on other govt department completely derailing the federal (and even state) govt budgets and plans.