Consider an economy with three types of individuals, differing only with respect to their preferences for monuments. Individuals of the first type get a fixed benefit of 100 from the mere existence of monuments, whatever their number. Individuals of the second and third type get benefits according to:
BII = 200 + 30 M - 1.5 M2
BIII = 150 + 90 M - 4.5 M2
where M denotes the number of monuments in the city. Assume that there are 50 people of each type. Monuments cost $3,600 each to build. How many monuments should be built?