Following the class example with the service function-t-10 + 0.01 V and demand f
ID: 1132061 • Letter: F
Question
Following the class example with the service function-t-10 + 0.01 V and demand function V-5000-1004 and discuss the following scenarios. Given that we know how to compute the new equilibrium point if the highway is improved such that the service function is changed to t-10+0.001V, we learn that the LOS is improved and more demand is accommodated. 4. a (10 pts) If the demand function is later found to underestimate the population, how would you modify the demand function? Please propose a plausible way of modifying the demand function and discuss your reason. b. (15 pts, graduate required, UG bonus) The coefficient for variable t in the demand function is set to be 100. How would you determine (or calibrate) this coefficient if you were to apply the analysis to a different city in which the travelers may have different behavior. Please propose a reasonable method for it.Explanation / Answer
From the service function t, we see that the amount of service increases with increase in demand for services V. The demand function shows that the level of demand declines with increasing amount of services provided. Thsi happens because amount of vservices provided also depends upon the quality of services. If the same demand could be fulfilled with lesser amount of the service provided, it means the quality of service has improved. This is illustrated by the example given where the service function is changed such that the coefficient of V decreases from 0.01 to 0.001. It can be found that this change in the service function leads to increase in demand.
Substituting t = 10 + 0.01V in V = 5000 - 100t , we get
V = 5000 - 100 ( 10 + 0.01V ) or V = 2000
After the improvement in highway, the new service function is t = 10 + 0.001V. Substituting this into the demand function, we get V = 3636.36.
Therefore, the improvement in quality leads increase in demand for services by 1636.36.
a) It is found that the demand function is underestimating the population. if the actual population is higher than what is taken into account by the demand function, the demand for services ought to be higher as well. Population here is an exogenous variable i.e. it is not determined within the system. Therefore, it cannot change the service function and the preferences of people regarding that service. So, the increase in population cannot be incorporated into the function by changing the coefficient of t. So, the increase in demand due to additional population will be taken into account by increase in the constatnt term in the demand function. Here, the constatnt 5000 is underestimating the population and it has to be increased to account for the actual population. Suppose 1% of the population is not accounted for, we increase the constatnt term by 1% and the demand function changes to V= 5050+ 0.01t. This is, of course, a crude example and the actual increase in the constatnt term may be different taking into consideration the effect of population on demand.
b) The coefficient of t in the demand function V depicts the sensitivity of demand to an increase in the amount of services provided. It shows that if t increases by 1 unit, the amount of services demanded will decrease by 100. As expalined earlier, the amount of services deamded indirectly depends on the service quality or the utility derived from consuming a certain amount of services. For example, if t depicts the deamnd for rafting services in a city, it may be more in a coastal city than in a city with few places for rafting. The travellers may visit a coastal city with the plan of doing some rafting. On the other hand, if the city is more famous for its churches and museums, the traveller may not have rafting on his itenerary. Therefore, the value of the coefficient of the rafting service function t will be lower in the demand function of a coastal city than that of the other. The decrease in demand due to a unit change in services will be less in the coastal town. With this example, we can say that the coefficient of t will be lesser in the demand function of a city where the service t is more desirable.
This analysis is based on the assumption that the demand function reamins the same for all cities ( as is apparent from the question). In reality, however, the differences in behaviour of travellers may be seen from different spec ifications of the demand function.