This brief note provides a simple, yet powerful example of how the marginal cost/marginal benefit principle can be used in everyday life. Using the decision of the optimal choice of speed on the highway, this note was developed for use as one of the first readings in an introductory microeconomics course. It is clear in this demonstration that marginal cost is increasing, while marginal benefit is decreasing, and how the intersection of these two curves shows the optimal choice. In addition, shifts in the curves can easily be demonstrated as an introduction to supply and demand.marginal analysis; economic education

Burkey, Mark L.

English

Research Papers in Economics

JOURNAL OF ECONOMICS AND FINANCE EDUCATION • Volume 7 • Number 2 • Winter 2008  1 
 
 
 
A Brief Introduction to Marginal Analysis for the 
Micro-Economics Principles Course 
 
Mark L. Burkey
1 
 
ABSTRACT 
 
This brief note provides a simple, yet powerful example of how the 
marginal cost/marginal benefit principle can be used in everyday life. 
Using the decision of the optimal choice of speed on the highway, this 
note  was  developed  for  use  as  one  of  the  first  readings  in  an 
introductory microeconomics course. It is clear in this demonstration 
that marginal cost is increasing, while marginal benefit is decreasing, 
and how the intersection of these two curves shows the optimal choice. 
In  addition,  shifts  in  the  curves  can  easily  be  demonstrated  as  an 
introduction to supply and demand. 
 
Introduction 
 
While each individual must make their own decision about how fast to drive, some general economic 
principles should be kept in mind. Here we describe some factors that enter into the decision. 
In general, we can boil down the costs and benefits of driving faster than the speed limit this way: 
Driving faster benefits us by saving time, but results in an increased risk of receiving a ticket and the 
associated pecuniary and non-pecuniary costs of a ticket. Additionally, as one drives faster there is an 
increased risk of an accident, and increased fuel costs. Most drivers ignore the increased fuel costs: While 
the cost of gas is significant, the marginal cost of fuel from driving faster is fairly small.
2 When a cost is so 
small that we can ignore it for decision-making purposes, economists usually call it a “second-order” cost. 
Let us construct a simple model for driving. Suppose that we need to drive exactly 60 miles, and get 
exactly 30 miles to the gallon. The road that we will be driving on has a speed limit of 55. The total cost of 
driving this distance will be 2 gallons of gas, plus some wear and tear on the vehicle, plus the value of our 
time. Therefore, the benefits of driving faster are reductions in this driving time. 
 
The Marginal Benefit of Driving Faster 
If we drive 55miles per hour, we can calculate the time that the trip will take in the following manner: 
 
(1) distance speed*time = , therefore  
(2) 
distance
time
speed
= , so time =60/55 = 1.091 hours. 
It may be more convenient to calculate the time in minutes. To do this, divide the speed by 60: 
 
                                                 
1 Mark L. Burkey, Associate Professor of Economics, Department of Economics and Finance, North Carolina A&T State 
University, Greensboro, NC  27411. 
 
2 The wind resistance on a vehicle is proportional to the square of speed, so you will use a little more gas per mile as you drive 
faster. In 1973 Richard Nixon signed a bill into law requiring a national speed limit of 55mph in order to save gasoline. Although 
repealed partially in 1987 and altogether in the 1990’s, in July 2008 a bill was filed in the U.S. Congress to reinstate a national 
speed limit. JOURNAL OF ECONOMICS AND FINANCE EDUCATION • Volume 7 • Number 2 • Winter 2008  2 
 
 
 
(3) 
60 3600
time 65.45
55/60 55
= = = minutes. 
 
Should we drive faster?  We first need to calculate the marginal benefit of driving faster. That is, we 
need to figure out how much additional time we save each time we go a little faster. We can start by 
calculating the time difference of increasing/decreasing our speed from 55 miles per hour in increments of 
2 miles per hour (using our cruise control): 
 
Table 1. Calculating the Marginal Benefit of Driving Faster 
Speed  Time 
Total time saved 
(compared to 55 
mph) 
Marginal 
Benefit 
53  67.92453  -2.47  -2.47 
55  65.45455  -------  ------- 
57  63.15789  2.30  2.30 
59  61.01695  4.44  2.14 
61  59.01639  6.44  2.00 
63  57.14286  8.31  1.87 
65  55.38462  10.07  1.76 
67  53.73134  11.72  1.65 
69  52.17391  13.28  1.56 
 
Notice that the marginal benefits are going down as you go faster and faster!  This is related to the idea 
that you must increase your speed by 100% in order to cut your driving time by only 50%. If we assume 
some dollar value for our time, say $.50 per minute, we can calculate the dollar value of the benefit of 
increasing our speed. 
 
The Marginal Costs of Driving Faster 
Of course, as you drive faster, your chances of being in a wreck, and the wreck being more serious 
increases with speed. Kloeden et al. (1997) found that for each additional 5km/hr (≈ 3 miles per hour) 
increase  in  speed,  the  probability  of  being  involved  in  a  serious  crash  involving  an  injury  doubles. 
However, the main cost on a driver’s mind is usually the cost of getting a ticket. In some states if you have 
no speeding tickets on your record, and you get one speeding ticket for no more than 9 miles per hour over 
the speed limit, you must pay the ticket and court costs, but your insurance rates will not go up. However, if 
you get a second ticket within 5 years, both tickets will increase your insurance. However, in some states 
you can remove one ticket from your record by going to “driving school”.  
So, if a driver has no tickets on their record, they could drive up to 64 miles per hour, and if ticketed, 
pay around $150 plus the lost time of being pulled over and mailing in the ticket. Driving a little faster than 
64 miles per hour would result in the same penalty, because you can normally go to court and “plea down” 
a ticket of up to 14 miles per hour over the speed limit down to 9 miles over. But, the cost increases when 
you factor in taking a day off of work and going to court (or hiring an attorney to do this for you). 
However, it is reasonable to expect that the probability of getting a speeding ticket is (almost) zero if 
you are within 5 miles of the speed limit. So, increasing your speed from 55 to 60 miles per hour would 
generate no additional risk of a ticket. In fact, in many cities, one can go at least 7 miles per hour over the 
speed limit, and face almost no chance of getting a ticket. Going 9 miles per hour over greatly increases 
your chances of a ticket. It is common practice that police officers will pull you over with certainty (if they 
see you) at 11+ miles over the speed limit. Of course, you could drive a long distance without even seeing a 
police car. If we were to put the previously mentioned costs and benefits on a graph, they might look like 
Figure 1 for a typical driver: JOURNAL OF ECONOMICS AND FINANCE EDUCATION • Volume 7 • Number 2 • Winter 2008  3 
 
 
 
 
Figure 1. Graphing the Marginal Cost and Benefit for Various Speeds 
 
 
Starting at a speed of 55 miles per hour, we should continue to go faster as long as the additional costs 
do not outweigh the additional benefits. According to the graph above, how fast should this driver go?  
(The marginal cost and marginal benefit curves intersect at around 65 miles per hour, suggesting that this is 
the optimal speed.)  However, suppose that the driver depicted in Figure 1 looked down at the speedometer 
and saw that he was going 69 miles per hour. What should he do, and why? (He should slow down, because 
the additional cost of speeding up to 69 far outweighs the additional benefits.) 
 
Shifts in the Marginal Benefit Curve 
 
How would your decision change if you were in a big hurry to get somewhere?  Perhaps you are late for 
work. The value of your time might increase from $.50 to $1.00. Looking at the graph above, what will 
happen to the marginal benefit curve?  How will this affect your speed?  How will this affect your risk of a 
ticket?  (Your marginal benefit of driving faster would increase, shifting the curve upward. The resulting 
optimal speed is higher. You are willing to take a higher risk of a ticket because of the situation.) 
 
Shifts in the Marginal Cost Curve 
 
Suppose that you will lose your insurance if you get another speeding ticket. How will that affect your 
marginal cost curve?  (The marginal cost of increasing your speed will be higher, shifting the marginal cost 
curve upward. This results in an optimal speed that is lower.)  
What if you can go to driving school and get a ticket removed?  Will this cause you to drive faster, or 
slower? (If the cost of going to driving school is lower than the cost of a ticket, it would lower the marginal 
cost of driving faster.) 
Lastly, suppose you buy a vehicle that is very safe, perhaps a Volvo Sport Utility Vehicle. How will 
that affect your driving behavior?  (Since you feel safer, the lower risk of injury will lower the marginal 
cost of speeding up, resulting in a faster optimal speed.) 
 
References 
Kloeden,  C.,  McLean,  A.,  Moore,  V.,  and  Ponte,  G.,  1997,  “Travelling  Speed  and  the  Risk  of  Crash 
Involvement,”  NHMRC  Road  Accident  Research  Unit,  The  University  of  Adelaide,  November  1997 
http://raru.adelaide.edu.au/speed, accessed 08/31/2008. 
 55  57  59  61  63  65  67  69  71  73 
Speed 
Marginal Benefit 
of going faster 
Marginal Cost of 
going faster   Value 
of time, 
money, 
risk to 
health 

A brief introduction to marginal analysis for the micro-economics principles course

Abstract

Similar works

Full text

Available Versions

Research Papers in Economics