Based on previous market research Metrojet (an airline) knows that there are two

Question

Based on previous market research Metrojet (an airline) knows that there are two types of travellers: those who make travel plans early E and last minute travellers L. Thus, it releases seates in its aircraft in two stages. The first stage occurs two months prior to a given travel date and the second occurs within two months of that same trawl date. Metrojet has estimated that the inverse demand for early travellers is given by PE = 500 - E. It has also estimated that the inverse demand for inverse demand for last-minute travelers is PL = 800 - 4L a seat, where L is the quantity of last-minute travellers (all prices are ind dollars). The airline has a total of 200 seates to allocate between these two types of travellers. Write down an expression for the total revenues that it can expect to receive from these 200 seats (assume all get filled). Use se your answer to the previous question to determine the optimal number of seats. What price must it charge each group? What is the price elasiticty of demand at this price? Suppose a colleague argues that, since early travellers are willing to pay upto 500 for a seat, all seats should be sold to these travellers. How should you respond to this claim?

Explanation / Answer

Pe =500-E Pl=800-4L and E+L =200 L =200-E revenue =Pe*E+Pl*L =500E-E^2 +800L-4L^2 =500E-E^2 +800(200-E)- 4*(200-E)^2 = 1300E-5E^2 hence for max revenue d R/dE =0 ie 1300-10E =0 hence E =130 ....... number of seats L =200-130 =70 ........ price of E =500-E =370 price of L =800-4*70 =520 elasticity of E=(dE/dp)*(P/E) =-1*(270/130) =-2.08 elasticity of L=(dL/dp)*(P/L) =(-1/4)*520/70 =-1.86 ...... revenue in this case is 1300E-5E^2 =84500 ....... if t 500 all E then revenue will be 500*200 =10000 ..... hence claim is true ..

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