For the given question though, they would have learnt in detail. I've never studied economics, here are my answers:
All you need to know is what a council does for a city.
Then just give some examples of tasks that large cities have to do that villages do not, and some examples of infrastructure which does not have economies of scale (if added gradually) such as sewage.
Max money = d/dN (sigmaN^0.5 - gammaN^2) = 0
=> 0.5sigma N^-0.5 - 2gammaN = 0
=> 0.5sigma N^-0.5 = 2gammaN
=> Sigma = 4gamma N^1.5
=> N = (sigma/4gamma)^(2/3)
Now where is my degree!
Road maintenance, sewage, lighting, policing contributions, maintainance of green spaces, development of infrastructure, planning permissions, administration of fines and tax etc...3ai) What does the co-ordination cost represnt?
All you need to know is what a council does for a city.
An exponent less than 1 means that the admin cost per head will fall continuously with population growth. In reality the cost per head does not call continuously, as the larger the population, the more complicated the administration of the city.3aii) Why should the exponent of N be greater than 1 for this term?
Then just give some examples of tasks that large cities have to do that villages do not, and some examples of infrastructure which does not have economies of scale (if added gradually) such as sewage.
Lets take sigma = 50 and gamma = 0.23bi)Draw a graph of costs per population
find optimal population
Max money = d/dN (sigmaN^0.5 - gammaN^2) = 0
=> 0.5sigma N^-0.5 - 2gammaN = 0
=> 0.5sigma N^-0.5 = 2gammaN
=> Sigma = 4gamma N^1.5
=> N = (sigma/4gamma)^(2/3)
Use above equation, needs to be profitable for city to occur.3ci) What sigma and gamma create peasant economies?
Technology, improving global economy, expectation of higher living standards3cii) Why do these values change over time
Technology improves implies bigger cities over time.3ciii) What does this say should happen to optimal city size over time
Now where is my degree!