Problem
From the ninth century B.C. until the proliferation of gunpowder in the fifteenth century A.D., the ultimate weapon of mass destruction was the catapult (John N. Wilford, "How Catapults Married Science, Politics and War," New York Times, February 24, 2004, D3). As early as the fourth century B.C., rulers set up research and development laboratories to support military technology. Research on improving the catapult was by trial and error until about 200 B.C., when the engineer Philo of Byzantium reports that by using mathematics, it was determined that each part of the catapult was proportional to the size of the object it was designed to propel. For example, the weight and length of the projectile was proportional to the size of the torsion springs (bundles of sinews or ropes that were tightly twisted to store enormous power). Mathematicians devised precise tables of specifications for reference by builders and by soldiers on the firing line. The Romans had catapults capable of delivering 60-pound boulders at least 500 feet. (Legend has it that Archimedes' catapults used stones that were three times heavier.) If the output of the production process is measured as the weight of a projectile delivered, how does the amount of capital needed vary with output? If the amount of labor to operate the catapult did not vary substantially with the projectile's size, what can you say about the marginal productivity of capital and returns to scale?
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.