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 250 from the mere existence of monuments, whatever their number. Individuals of the second type get benefits according to BII = 30M - 2M2 for M < 2, but BII = 200 + 30M - 2M2 for M ≥ 2. Individuals of the third type get benefits of BIII = 150 + 90M - 4M2 where M denotes the number of monuments in the city. Assume that there are 50 people of each type. Monuments cost $3,000 each to build. How many monuments should be built?