Task III Consider an economy with three types of individuals, differing only with respect to their preferences for dikes. Individuals of the first type get a fixed benefit of 250 from the mere existence of dikes, whatever their number. Individuals of the second type get benefits of BiI = 300 + 90D - 4D2 where D denotes the number of dikes in the city. Individuals of the third type get benefits according to Biii = 30D 2D2 for D 2. Assume that there are 50 people of each type. Dikes cost $3,000 each to build. How many dikes should be built? [12 points] Task III Consider an economy with three types of individuals, differing only with respect to their preferences for dikes. Individuals of the first type get a fixed benefit of 250 from the mere existence of dikes, whatever their number. Individuals of the second type get benefits of BiI = 300 + 90D - 4D2 where D denotes the number of dikes in the city. Individuals of the third type get benefits according to Biii = 30D 2D2 for D 2. Assume that there are 50 people of each type. Dikes cost $3,000 each to build. How many dikes should be built? [12 points]