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Unformatted text preview: Urban Economics: Economics 4621 University of Minnesota, Spring 2004 N11: Notes on Congestion MODEL WITH FIXED CAPACITY Suppose that there is a highway that connects the suburbs to the downtown. Let Q denote the number of drivers on this road. The time cost per driver A ( Q ) (the average time cost) depends upon the number of drivers. Assume A ( Q ) = 0 for Q X (where X is referred to as capacity) and A ( Q ) > for Q > X . T h i s captures the idea that when there are few cars on the road, the addition of another car makes no difference for congestion. But after a certain point, addition of cars begins to congest the highway and commute times goes up. Total time cost is T ( Q ) = A ( Q ) Q. and marginal time cost is M ( Q ) = T ( Q ) = A ( Q ) + A ( Q ) Q . The marginal time cost equals the average time cost plus the change in average cost multiplied by the number of drivers. Let D ( Q ) be note the inverse demand for driving when prices are denoted in units of time. This is the marginal willingness to pay (in time) for theof time....
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