We assume that in a village there are farmers, carpenters, and tailors, who provide the three essential goods: food, housing, and clothing. suppose the farmers consume 2/5 of the food (produced by farmers), 1/3 of the housing (produced by carpenters) and 1/2 of the clothes (produced by tailors). the carpenter consumes 2/5 of the food, 1/3 of the housing, and 1/2 of the clothes. the tailors consume 1/5 of the food, 1/3 of the housing, and no clothes. assume this is a closed leontief model.
if we know that the tailors produce 688 units of clothes,
then the farmers produce units of food,
and the carpenters produce units of housing.

If p(x) is the total value of the production when there are x workers in a plant, then the average productivity of the workforce at the plant is a(x) = p(x) x . (a) find a'(x). a'(x) = xp'(x) − p(x) x a'(x) = xp'(x) − p(x) x2 a'(x) = p'(x) − p(x) x a'(x) = xp'(x) − p'(x) x2 a'(x) = p'(x) − xp(x) x2 why does the company want to hire more workers if a'(x) > 0? a'(x) > 0 ⇒ a(x) is ; that is, the average productivity as the size of the workforce increases. (b) if p'(x) is greater than the average productivity, which of the following must be true? p'(x) − xp(x) > 0 p'(x) − xp(x) < 0 xp'(x) − p'(x) > 0 xp'(x) − p(x) < 0 xp'(x) − p(x) > 0