Answer to Question #277464 in Economics of Enterprise for emem

Question

Case Study 1 – The Economic Daytime Running Light 

75% of driving takes place during the daytime. 

2% of fuel consumption is due to accessories (radio, headlights, etc.). Cost of fuel = $4.00 per gallon. 

Average distance traveled per year = 15,000 miles. 

Average cost of an accident = $2,800. 

Purchase price of headlights = $25.00 per set (2 headlights). 

Average time car is in operation per year = 350 hours. 

Average life of a headlight = 200 operating hours. 

Average fuel consumption = 1 gallon per 30 miles. 

Answer the following set of questions: 

1. What are the extra costs associated with driving with headlights on during the day? 

2. What are the benefits associated with driving with headlights on during the day? 3. What additional assumptions (if any) are needed to complete the analysis? 4. Is it cost effective to drive with headlights on during the day?

Answer 1

1.Annual fuel cost $= (\frac{15,000 mi}{yr})\cdot (\frac{1 gal}{30 mi})\cdot (\frac{\$2.00}{gal}) = \$1,000/yr.$

Assume (worst case) that $2\%$ of fuel consumption is due to normal (night-time) use of headlights.

Fuel cost due to normal headlights $= (\frac{\$1,000}{yr})\cdot (0.02) = \$20 /yr$

Fuel cost due to continuous use of headlights$= (4) (\$20/yr) = \$80/yr.$

Headlight cost for normal use $= (0.25) ( \frac{350 hr/ yr }{200 hr/ yr})( \$ 25 set ) = \$10.94/yr.$

Headlight cost for continuous use $= (\frac{ 350 hr/ yr }{200 hr/ yr})( \$ 25 set ) = \$43.75/yr.$

Total cost associated with daytime use$= (\$ 80−\$ 20)+(\$ 43.75−\$ 10.94) = \$92.81/yr$

The extra costs of driving with headlights on during the day include increased fuel consumption and more frequent headlight replacement.

2. Headlights increase visibility to other drivers on the road as well as reducing the chance of an accident.

Additional assumptions needed to consider during our analysis of the situation include:

i) the percentage of fuel consumption due to headlights alone

ii) how many accidents can be avoided per unit time. 

If driving with your headlights on during the day results in at least one accident being avoided during the next $\frac{ (\$2,500)}{(\$92.81)}= 27 years$ , then the continuous use of your headlights is cost effective.