3.a. Specialization and trade. An exponent less than one would imply that a system with more elements has a lesser coordination complexity than each element acting independently. Such would only be possible if humans became telepathic when forced into close proximity.
3.b. Consumption per person would be equal to the usable output of each person, minus overhead losses, minus stockpiling and savings. Assuming the latter to be zero, consumption is x = sigma N^0.5 - gamma N^2. To find minima and maxima, we take the first derivative with respect to N, and find where it is zero. 0.5 sigma N^-0.5 - 2 gamma N = 0. The non-imaginary solution is N=(sigma/4 gamma)^(2/3).
3.c. Plug N=2 into the above equation. To support cities of that size, gamma must be less than 9% of sigma. Sigma may be increased by gains in productivity, such as with specialization. Gamma may be reduced by lowering coordination burdens, such as by using money instead of barter, or employing merchant specialists. Changes in gamma have a greater effect on city size, so given the equal-cost choice between a universal education mandate and a guaranteed uniform currency standard, the latter is preferable, if larger cities are desired.
If student economists cannot think their way through that problem, we may assume that they will have a detrimental future effect upon both sigma and gamma, and we should therefore kill them now before they cause our cities to collapse. Judging by Detroit, we may already be too late.
Agree on both counts. This question seems to have an appropriate level of difficulty for the student rank and written in a fairly intelligible manner. Can't speak to the rest of the test, but I don't find this question off sides at all. And yes it is very likely too late.
3.a. Specialization and trade. An exponent less than one would imply that a system with more elements has a lesser coordination complexity than each element acting independently. Such would only be possible if humans became telepathic when forced into close proximity.
3.b. Consumption per person would be equal to the usable output of each person, minus overhead losses, minus stockpiling and savings. Assuming the latter to be zero, consumption is x = sigma N^0.5 - gamma N^2. To find minima and maxima, we take the first derivative with respect to N, and find where it is zero. 0.5 sigma N^-0.5 - 2 gamma N = 0. The non-imaginary solution is N=(sigma/4 gamma)^(2/3).
3.c. Plug N=2 into the above equation. To support cities of that size, gamma must be less than 9% of sigma. Sigma may be increased by gains in productivity, such as with specialization. Gamma may be reduced by lowering coordination burdens, such as by using money instead of barter, or employing merchant specialists. Changes in gamma have a greater effect on city size, so given the equal-cost choice between a universal education mandate and a guaranteed uniform currency standard, the latter is preferable, if larger cities are desired.
If student economists cannot think their way through that problem, we may assume that they will have a detrimental future effect upon both sigma and gamma, and we should therefore kill them now before they cause our cities to collapse. Judging by Detroit, we may already be too late.