U.S.Supreme Court Justice examines government's role in controlling & managing health risks. One major problem examined is cleanup of hazardous waste sites. He wish to see waste sites 100% clean.

a. Explain, using theory of optimization & a graph, the circumstances under which waste site could be made "too clean".
b. Justice Breyer believes that a society can enjoy virtually all health benefits of cleaning up a waste site for only a "small fraction" of the total cost of completely cleaning site. Using graphical analysis, illustrate this situation. (Hint: Draw MB and MC curves with shapes that specifically illustrates this situation.)

a. The theory of optimization suggests that there is an optimal level at which a waste site should be cleaned, beyond which it becomes "too clean." To understand this concept, let's consider a graph where the x-axis represents the level of cleanliness of the waste site, and the y-axis represents the cost of cleaning.

Initially, as the site gets cleaner, the cost of cleaning decreases since the most significant and obvious hazards are addressed first. However, as the site approaches 100% cleanliness, the cost of further cleaning increases significantly. This is because achieving absolute cleanliness involves diminishing returns, where the remaining contaminants are harder to remove and require more resources.

On the graph, we can plot the cost of cleaning (MC curve) as a downward-sloping curve, indicating diminishing marginal costs. Initially, the curve is relatively steep, indicating high costs. As the cleanliness level increases, the curve flattens, indicating lower additional costs but still increasing.

To find the point at which the waste site becomes "too clean," we need to consider the benefits side as well. If the marginal benefit (MB) of cleaning the waste site is relatively flat or decreasing as the cleanliness level approaches 100%, it suggests that the additional health benefits gained from further cleaning become minimal or even negligible.

b. Justice Breyer's belief that a society can enjoy most health benefits of cleaning up a waste site for only a small fraction of the total cost of complete cleaning can be illustrated graphically. On the same graph as before, we can now plot the marginal benefits (MB) and marginal costs (MC) curves.

The MB curve, representing the additional health benefits gained from cleaning the site, should be steeper initially, indicating substantial benefits. However, as the cleanliness level increases, the curve starts to flatten, indicating that the additional health benefits become relatively smaller.

On the other hand, as mentioned previously, the MC curve representing the cost of cleaning decreases initially but eventually starts to increase as the cleanliness level approaches 100%.

The graphical analysis would show the point where the MB curve intersects the MC curve initially, indicating the optimal level of cleanliness where the marginal benefits and marginal costs are balanced. However, as the cleanliness level progresses, the MB curve would start to flatten out before the MC curve. This indicates that substantial health benefits can be achieved for a relatively small fraction of the total cost of complete cleaning.

By illustrating this situation graphically, it becomes clear that there is a threshold where the additional cost of achieving absolute cleanliness outweighs the marginal health benefits gained. Hence, it supports Justice Breyer's belief that society can enjoy most health benefits at a fraction of the cost of complete cleanup.