Harry and kim run the only two grocery stores in the small town of ida mae, iowa. both sell cola to all of the locals. there are two choices for each store owner, they can charge a low price and hope that their competitor does not follow suit and charge a low price as well. or, they can charge a high price. the profits earned by the two store owners are listed below, with harry’s profits listed first in each cell.
kim’s store
low price; high price
low price 10, 10; 70, 20
harry’s store
high price 20, 70; 50, 50
a. in terms of their collective interest, what is the best outcome here? is this outcome a nash equilibrium? expalin.
b. suppose that the two stores are closed on sunday. suppose further that they reach the following agreement – harry will charge a low price while kim charges a high price on monday, wednesday and friday. on tuesday, thursday and saturday, the positions will be reversed. if they employ this strategy, what will each store’s average profit per day be?
c. now, the strategy described in (b) may work well for a short period of time. but, eventually, consumers will catch on and notice that harry always charges a lower price on monday, wednesday and friday while kim charges the low price on tuesday, thursday and saturday. if consumers then alter their behavior in order to take advantage of the price discrepancy, the profit rates in the cells will change. thus, in order to keep consumers from knowing which store is charging the lower price on any given day, suppose that harry and kim agree to randomly select their prices each day. if they each agree to charge the low price 2/3 of the time and the high price 1/3 of the time, what will each firm’s average profit per day be? how does this compare with what they could have expected to earn in (b)?