In constructing a new building, the building contractor must decide what technology to
use the mitigate the noise pollution that the construction would cause. Assume that typ-
ical street noise without any construction is 60 decibels (dB), while the street noise while
the construction is going on would be 110 dB without any noise-mitigating technology.
The cost of constructing the building while maintaining a street noise level of x dB (for x
between 60 and 110) is T C(x) = 1, 000, 000 + (110 −x)2, measured in Australian dollars.
The total externality cost of experiencing x dB (for x between 60 and 110) of street noise
for nearby residents would be Ext(x) = [(x−60)(x−59)]/2

(a) Find a formula f (x) for the difference T C(x) −T C(x + 1). Carefully discuss what
f (x) approximately represents