Question

In April 2010 the BP Deepwater Horizon oil rig suffered a failure in its subsurface blowout preventer leading to an explosion. Eleven workers died and approximately 4.9 million barrels of oil leaked into the Gulf of Mexico. The spill had a substantial impact on nearby coastal areas, including a sharp decrease in the number of visitors to the Gulf coast in the year following the oil spill. The following information describes the average cost of traveling to New Orleans (NOLA) from various regions of the United States along with visit rates before and after the oil spill.

Region Population Total Cost of Trip Visit Rate Before Spill Visit Rate After Spill
SE 400 $33 0.56 0.14
MW 1,200 $52 0.43 0.11
NE 800 $71 0.29 0.07


In addition, the following equations characterize the relationship between visit rates and total cost:

Before Spill: rate = 0.79 - 0.007*cost

After Spill: rate = 0.21 - 0.002* cost

a) How many people visiting NOLA before and after the oil spill?

b) How many people would have visited NOLA before and after the oil spill if the city had charged visitors a flat fee of $10 upon entry?

c) Estimate the cost of the oil spill to New Orleans. Assume linear demand and ignore the 11 fatalities.

Answer 1

a) To determine the number of people visiting NOLA before and after the oil spill, we need to calculate the visit rates using the given equations and the total cost of the trip for each region.

For the SE (Southeast) region:

Before Spill:

rate = 0.79 - 0.007 * cost

rate = 0.79 - 0.007 * $33

rate = 0.79 - $0.231

rate = 0.559

After Spill:

rate = 0.21 - 0.002 * cost

rate = 0.21 - 0.002 * $33

rate = 0.21 - $0.066

rate = 0.144

Number of people visiting NOLA in the SE region before the spill:

400 * 0.56 = 224

Number of people visiting NOLA in the SE region after the spill:

400 * 0.14 = 56

For the MW (Midwest) region and NE (Northeast) region, we perform the same calculations:

MW region:

Before Spill:

rate = 0.79 - 0.007 * cost

rate = 0.79 - 0.007 * $52

rate = 0.79 - $0.364

rate = 0.426

After Spill:

rate = 0.21 - 0.002 * cost

rate = 0.21 - 0.002 * $52

rate = 0.21 - $0.104

rate = 0.106

Number of people visiting NOLA in the MW region before the spill:

1,200 * 0.43 = 516

Number of people visiting NOLA in the MW region after the spill:

1,200 * 0.11 = 132

NE region:

Before Spill:

rate = 0.79 - 0.007 * cost

rate = 0.79 - 0.007 * $71

rate = 0.79 - $0.497

rate = 0.293

After Spill:

rate = 0.21 - 0.002 * cost

rate = 0.21 - 0.002 * $71

rate = 0.21 - $0.142

rate = 0.068

Number of people visiting NOLA in the NE region before the spill:

800 * 0.29 = 232

Number of people visiting NOLA in the NE region after the spill:

800 * 0.07 = 56

b) If the city had charged visitors a flat fee of $10 upon entry, the cost of the trip for each region would increase by $10. We can then recalculate the visit rates and determine the number of people visiting NOLA using the updated cost.

For the SE region:

Before Spill:

rate = 0.79 - 0.007 * (cost + 10)

rate = 0.79 - 0.007 * ($33 + $10)

rate = 0.79 - $0.469

rate = 0.321

After Spill:

rate = 0.21 - 0.002 * (cost + 10)

rate = 0.21 - 0.002 * ($33 + $10)

rate = 0.21 - $0.086

rate = 0.124

Number of people visiting NOLA in the SE region before the spill with the flat fee:

400 * 0.321 = 128

Number of people visiting NOLA in the SE region after the spill with the flat fee:

400 * 0.124 = 50

Performing similar calculations for the MW and NE regions, we find:

MW region:

Number of people visiting NOLA in the MW region before the spill with the flat fee:

1,200 * 0.258 = 309

Number of people visiting NOLA in the MW region after the spill with the flat fee:

1,200 * 0.064 = 77

NE region:

Number of people visiting NOLA in the NE region before the spill with the flat fee:

800 * 0.213 = 170

Number of people visiting NOLA in the NE region after the spill with the flat fee:

800 * 0.037 = 30

c) To estimate the cost of the oil spill to New Orleans, we need to calculate the difference in the number of visitors before and after the spill and multiply it by the average cost of the trip.

For the SE region:

Cost difference = ($33 - $10) = $23

Number of visitors difference = 224 - 56 = 168

Estimated cost for the SE region = Cost difference * Number of visitors difference

Estimated cost for the SE region = $23 * 168 = $3,864

Performing similar calculations for the MW and NE regions, we find:

MW region:

Cost difference = ($52 - $10) = $42

Number of visitors difference = 516 - 132 = 384

Estimated cost for the MW region = Cost difference * Number of visitors difference

Estimated cost for the MW region = $42 * 384 = $16,128

NE region:

Cost difference = ($71 - $10) = $61

Number of visitors difference = 232 - 56 = 176

Estimated cost for the NE region = Cost difference * Number of visitors difference

Estimated cost for the NE region = $61 * 176 = $10,736

Step-by-step explanation: