Uniqueness Theorems In Linear Elasticity

Question: Discuss about a Report on Uniqueness Theorems In Linear Elasticity? Answer: Linear Elasticities If the fare of the express bus rises, then the demand for the express bus will fall. Now, here in the table, data on arc elasticity are given. The demand for the trips can be calculated by the trips in the pick hours. Here total number of trip is 4000. This is split between the express and the local bus in a ratio of 40: 60. Now, total trips for express bus is, 4000 * (40 / 100) = 1600 Total number of trips of local bus is, 4000 * (60 / 100) = 2400 Price for travelling by express bus is, say, Pe = 1 On the other hand, price for travelling by local bus is, say, Pl = .50 1. Now, the fare of the express bus has been raised from $ 1 to $ 1.50. The formula for arc elasticity of demand is, E = % change in demand for express bus / % change in fare of express bus -.15 = % change in demand for express bus / ((1.50 1) / (2.50/2)) % change in demand for express bus = -.15 * (.50/1.25) So, percentage change in demand for express bus = (-0.15) * 0.4 = .06 % Therefore, the demand will fall by .06 % due to the rise in the fare of ticket of express bus. Total number of trips of express bus will fall by .06%*1600 = .96 On the other hand, the demand for the local bus will rise. Elasticity = % change in the demand for local bus / % change in the fare of express bus So, .02 = % change in the demand for local bus / 0.4 So, % change in the demand for local bus = 0.2 * 0.4 = .08 % The demand for the local bus will rise by .08% Trips of local bus will rise by .08%*2400= 1.9 =2 (approx) 2. The travel time for the express bus has fallen from 30 minutes to 25 minutes. So, the demand for express bus will rise. Now, arc elasticity = % change in demand for express bus / % change in the travel time of express bus - .08 = % change in demand for express bus / ((25 30)/ ((30 + 25) / 2)) So, % change in demand for express bus = (-.08) * ((-5) / (55 / 2)) = .0144 Here it is seen that the demand for express bus will rise by .0144 % due to fall in the travel time of express bus (Knops and Payne, 2012). Trips for express bus will rise by .0144%*1600= 0.23 On the other hand, the demand for the local bus will fall immediately. Ark elasticity = % change in the demand for local bus / % change in the travel time of express bus So, .01 = % change in the demand for local bus / ((25 30)/ ((30 + 25) / 2)) % change in the demand for local bus = .01 * ((-5) / (55 / 2)) = -.0018 % Therefore, here it is seen that the percentage of demand for the local bus will fall by .0018% Trips of local bus will fall by .0018%*2400= .04 3. It is assumed that the data of arc elasticity are actually point elasticity. Now, if the express bus fare rises from $1 to $1.30, then the demand for express bus will fall and the demand for the local bus will rise. If the local bus fare is reduced, then the demand for the express bus will fall and the demand for the local bus will rise (Eringen and Suhubi, 2013). Effect of rise in the express bus fare Elasticity = % change in demand for express bus / ((1.30-1) / 1) So, % change in demand for express bus = -.15 * .30 = -.045% Therefore, the effect of change in express bus fare is .045% reduction in the demand for express bus. Trips of express bus will fall by .045%*1600= .72 Local bus demand will rise. Elasticity = % change in the demand for local bus / ((1.30-1) / 1) So, % change in the demand for local bus = .02 * .30 = .006% The demand for local bus will rise by .006% Trips of local bus will rise by .006%*2400= .144 Effect of fall in the local bus fare Demand for express bus will fall. Elasticity = % change in the demand for express bus / ((.50-.40)/.50) So, % change in the demand for express bus = .62 * .02= .0124% The demand for express bus will fall by .0124% Trips of express bus will fall by .0124%*1600= .198=.2 (approx) The demand for local bus will rise. Elasticity = % change in the demand for local bus / ((.50-.40)/.50) So, % change in the demand for local bus = - .03 * .02 = -.0006% Therefore, the demand for local bus will rise by .0006%. Trips for local bus will rise by .0006%*2400= .0144. Reference List Knops, R. J., and Payne, L. E. (2012).Uniqueness Theorems In Linear Elasticity(Vol. 19). Springer Science Business Media. Eringen, A. C., and Suhubi, E. S. (2013).Linear theory. Academic press.