Question

Problem 1. Two Sandwich shops, Early Sandwich (ES) and Best Sandwich (BS), sell identical sandwiches and are located side-by-side in State College. Every morning, ES opens at 8am and advert ises its sandwich price pES on a billboard outside the store. BS opens at 9am, observes ES's daily price, and advertises its daily prices pBs on its store's window. BS faces a unit cost of 3 while ES faces a unit cost of 2 for making a sandwich. The market (inverse) demand for sandwiches is P 80-2Q 1. Suppose ES and BS operate for only one day. That is, they open, sell their sandwiches, collect profits, and close down forever. Characterize BS's best response function. Char- acterize the equilibrium strategy profile of this game and resulting equilibrium prices, quantities, and profits in this market. Is this outcome (Pareto) efficient? Explain 2. Suppose now ES and BS get two years to operate. At the end of this time they both shut down and move on to other markets. Both firms care about the total profits earned during the course of the whole year (e.g. the sum of daily profits). They do not discount future revenue. How would daily prices change? How much more profit do they earn? 3. Would ES prefer to post prices at 9am? Explain 4. Suppose a new town ordinance lets ES and BS stay and sell sandwiches forever, how ever they must now open at the same time (e.g. set prices simultaneously each day) Moreover, BS has made a new contract with ES's supplier so that they now both face a unit cost of $2 for making a sandwich. Both firms now discount future profits at a rate E (0, 1). Describe and equilibrium in which both firms make positive profits. Derive one such equilibrium, noting both the strategies, equilibrium prices, discounted profits, and quantities sold in each period.

Answer 1

Giveno- a) Market demand for sandwiches :- P = 80 - 29 b) Unit cost of ES = 2 c) Unit cost of BS = 3 1 Answero- OBS's best response - Keeping the price of sandwich at a lower cost than Es in order I to attract more customers and earn the maximum profit. This outcome will be efficient since lower the price, higher will be the demand for Sandwiches . Equilibrium quantity &- 38 sandwiches د نو طنا نیرع 4 =ة ع نوم Reason: If BS selles sells 39 sandwiches then , p = 80 -2(39) = 80-78=2(which is lesser than the cost) oor 39 as equilibrium quantity is not applicable. But when @= 38 ; p = 80 (2x38)=80-76 Scanned with CamScanner

Wassmate Dott. Page Change in daily prices. - a) Since ES opens at 8 am and BS opens of I am, then Es can charge a hgher price flom 8am-am since there is no other Sandwich seller. b) Es can earn more profit befor BS as Es can charge any amount from 8an to gam and along with the unit cost of Es is 2 which is less than BS.' of Yes, Es prefer to post prices at 9 am because at that time BS will enter the market for selling sandwiches and hence to attract customers, Es will charge lesses that what it was charging from 8am - I am. This would maximise the profit for of Es. 6 Giveno- Unit cost of both es and BS=0 Therefore, post gam, ES and BS should sell at the same price in order to make profits. Equilibriumpsite quantity. -_38 Equilibrium price on 4 Issolution :- Refer to the reason (part 1 answer CamScanner