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) = [(x60)(x59)]/2

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

(b) Find a formula g(x) for the difference Ext(x) Ext(x 1). Carefully discuss what g(x) approximately represents.

(c) Using your answers to parts (a) and (b), find the efficient level of noise pollution in decibels.