Question

There are two hotels in town, Gilton and Tadisson. Each hotel offers two services: a room to spend the night in, and a meal in its restaurant. These hotels are not differentiated, thus offering identical products, and customers choose to stay at the hotel where they get the highest surplus (usually, the hotel with the cheapest prices). If customers were to get the same positive surplus from staying at either hotel, then we assume that half of them go to one hotel and half go to the other one Morcover, suppose that it only makes sense for a consumer to have a mcal at a hotel if he or she happens to be staying at that hotel To simplify, suppose there are no fixed costs, and that the MC of a room is 10 and the MC of a meal is 5, for both hotels. The hotels must determine what price to charge for the room and what price to charge for the meal, and the choice of prices is simultancous Suppose there are 10 customers, which we call of type A, with the following willingness to pay for a room and a meal at either hotel: Туре Room A Meal $100 $25

Answer 1

there are two identical hotels with no diffentiation of services. customers will go to hotel will cheapest rate. therefore (All amounts are in $, MC , Marginal cost) Hotels costs are & MC of room no Mc of meal: 5 a) In this situation following willing ness to pay. there are 10 with customers type Room meal 25 100 at the hotel Now as given consumer will have a meal at which he will stay, therefore first price decision for hotels is deciding soom price. play off table. following is per sustomer Gilton Price / tadission price highest price (100) lowent price (40) 60,60 -40,0 Highest Price 1100) 0,-40 lowest price 140)

(2) While hotels can charge any amount between 100 (max price) to lowest price 401MC), pay off table is focused on these theso boundary conditions. Now, as shown of one hotel charges higher than other hotel it will lose all customers. therefore Mash equilibrium is cool with both charging no porce profit per costomer =0 thus 5 customers cooll go to Hotel Goiton and sto tadssion However since these customers will have meal at the respective hotels only, hotels will charge maximum price of meal. Meal perce=25 profit from meal per customer = 20 total profits .5*20 = 100 Now if hotels Consifito te meal as add-on and advertise only soom price, Total Mc will be = 40 45 = u5 Also customer willings to pay will be = 100+25 = 125 b

following is per customer play off table. Giton pricel tadission price Highest price(125) Cowest price(us) Highest price (125) -45,0 80,80 0,0 lowest price lus O, -45 While hotels can charge any amount betweent 20 (max price) to lowest parce 45 CHC), pay off table focused on these two boundary conditions. Now, as shown if one hotel charges higher than other hotel it will lose all the customers. therefore Nash equilibrium is cool with bath charging 45 price. profit per customer to ( In this situation customers with there are two types of following willingness type Room real total 100 25 125 35 ५०

Since total willingness of customer type B is lower than even Mc us, hotels will not be able to serve them for type A customer situation is similar to situation b. thus resulting in o profits per customer. this is because willingnen to pay for type B customer is not enough to cover for loss in lower Room price. Had the willing hest for meal been greater than 10, then total would be ust and hotels will be able serve them for ado on service this even if type B customers couldn't affood room (MC=40735) because of add on service, they will be served and hotels will get economic profit. However its not possible toget sustain profits greate than o Since other hoted can under cut prices equal to total Mc. This situation a is best case for positive profite