Travel Cost Example
Let the inverse demand for fishing in a given lake be:
Df = 200  10t + 110c,
where t is the number of trips, c is the catch per day (a measure of quality), and Df is
measured in $/trip. Answer the following questions, always explaining or showing your
work.
1. Let c = 5, and suppose all fishers incur a travel cost of at least $10/trip. How many
trips will recreational fishers take to this lake? What will be the consumers’ surplus (CS)
associated with this level of use? [You might want to draw a diagram to help you answer
this.]
2. Now suppose c rises to 10. Repeat #1. [This is especially easy if you answer #1 for
arbitrary c, i.e. express both t* and CS as functions of c, into which you can plug c=5 and
c=10.] The principle illustrated here is that increasing the quality of the amenity
increases its travel-cost valuation.
3. Now go back to #1 and redo it under the assumption that the minimum travel cost to
the lake is $20/trip.
Answers on the next page—don’t peek!
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Answers:
1. I don’t have time to draw a picture, so we’ll just have to wing it without one. For me,
the easiest way to do this is to solve the problem in its most general form, and then just
plug in numbers as needed. So I’ll solve it for arbitrary c (quality) and p (minimum travel
cost). So start out by setting p = 200  10t + 110c and solving for t.
10t = 200 + 110c  p
 t* = 20 + 11c  p/10
Df is the inverse demand function, but this is the actual demand function: give me a price
and I’ll return a quantity. Now, for CS, we have to imagine a triangle whose base is t*
and whose height stretches from p at the bottom, up to the vertical intercept of Df, 200 +
110c at the top. Therefore,
CS = ½bh = ½  (20 + 11c  p/10)  (200 + 110c  p) = ½  10t*2 = 5t*2
So for c = 5 and p = $10/trip,
t* = 20 + (11)(5)  (10/10) = 20 + 55 – 1 = 74 trips
CS = 5  (74)2 = $27,380
2. Now c = 10:
t* = 20 + (11)(10)  (10/10) = 20 + 110 – 1 = 129 trips
CS = 5  (129)2 = $83,205
Improving the quality of the lake increases its value to recreationists, as well as the
number of trips they want to take there.
3. Now c = 5 again, but p = 10:
t* = 20 + (11)(5)  (20/10) = 20 + 55 – 2 = 73 trips
CS = 5  (73)2 = $26,645
As compared to the initial situation, raising the minimum travel cost reduces both the
number of trips and the value of the amenity to recreationists. But it doesn’t reduce it by
much. This makes sense if you compare the $10/trip change in minimum travel cost to
the vertical intercept of inverse demand Df, which is 200 + 110(5) = $750/trip when c = 5.
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