Question

e. Suppose that your company hires an economist to analyze passenger demand. The economist discovers two distinct classed of passengers. The first class is comprised of business travelers who must travel this route for their companies. The demand function for business travelers is QB = 1200 - 0.2PB. The second class is comprised of people on vacation. Their demand function is QV = 800 - .8PV. Also, assume that your company can price-discriminate between the classes of passengers. Using the original cost function, determine the ticket prices for each class of passenger. How many business and vacation travelers will sail on your ship at these prices?

Answer 1

Consider the given problem here there are two types of consumer one is “business class” having demand curve, “Qb = 1200 – 0.2*Pb, => Pb = 6,000 – 5*Qb” and “2^nd class” having demand curve, “Qv = 800 – 0.8*Pv,

=> Pv = 1000 – 1.2*Qv”.

Now, there is a fixed cost of “500,000” and per unit cost of “500”, => the total cost function is given by, “TC=500,000 + 500*Q”, => MC = 500. Now, here the monopolist can discriminate between consumer, => the monopolist can charge different price to different consumers. So, here the optimum condition to set the “P” that will maximize the total profit is given below.

=> MRb = MRv = MC.

So, here “Pb = 6,000 – 5*Qb”, => TRb = Pb*Qb = 6,000*Qb – 5*Qb^2, => MRb = 6,000 – 10*Qb”.

Now, “Pv = 1000 – 1.2*Qv”, => TRv = Pv*Qv = 1,000*Qv – 1.2*Qv^2, => MRv = 1,000 – 2.4*Qv”, and MC=500.

So, by MRb = MC, => 6,000 – 10*Qb = 500, => 6,000 -500 = 10*Qb, => Qb = 5500/10 = 550.

Now, by MRv = MC, => 1,000 – 2.4*Qv = 500, => 2.4*Qv = 500, => Qv = 208.33.

So, the optimum quantity choice is, “Qb=550” and “Qv=208.33”.

So, at “Qb=550” the corresponding “Pb=6000 – 5*550 = 3250” and at “Qv=208.33” the corresponding “Pv=1000 – 1.2*208.33 = 750.004.

So, given the situation the optimum price of “business” and “vacation” classes are “Pb=$3250” and “Pv=$750.004” respectively and corresponding sail are “Qb=550” and “Qv=208.33”.