A particular road is used by N drivers each day. Each driver obtains a benefit v from the journey and incurs a cost c(N) that increases with the number of drivers on the road due to congestion. Suppose that the cost incurred is given by c(N) a + bN, for some positive numbers a, b. If the agent decides not to use the road, they receive 0. You may assume throughout that the number of drivers N can be any real number (rather than an integer). Each driver uses the road at most once. (ii) Show that the number of drivers that join the road is V - a Ne =

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter7: Uncertainty
Section: Chapter Questions
Problem 7.8P
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A particular road is used by N drivers each day. Each driver obtains a benefit v from the journey and
incurs a cost c(N) that increases with the number of drivers on the road due to congestion. Suppose that
the cost incurred is given by
c(N)
= a + 6N,
for some positive numbers a, b. If the agent decides not to use the road, they receive 0. You may assume
throughout that the number of drivers N can be any real number (rather than an integer). Each driver
6,
uses the road at most once.
(ii) Show that the number of drivers that join the road is
а
Ne
Transcribed Image Text:A particular road is used by N drivers each day. Each driver obtains a benefit v from the journey and incurs a cost c(N) that increases with the number of drivers on the road due to congestion. Suppose that the cost incurred is given by c(N) = a + 6N, for some positive numbers a, b. If the agent decides not to use the road, they receive 0. You may assume throughout that the number of drivers N can be any real number (rather than an integer). Each driver 6, uses the road at most once. (ii) Show that the number of drivers that join the road is а Ne
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