Harry and Kim run the only two grocery stores in the small town of Ida Mae, Iowa
ID: 1118635 • Letter: H
Question
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? Explain. (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)?
Harry and Kim run the only two grocery stores in the small town of Ida Mae, lowa. 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 High Price 70, 20 Low Price Low Price 10, 10 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? Explain. (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,Explanation / Answer
a) In terms of collective interest of Kim and Harry, 4th cell shows the best outcome when profits of both are 50 each with total profit equal to 100. No, it is not the Nash equilibrium also , as the charging low price is the dominant strategy which earns more profit for both, even if the other charges high profit. Thus, this outcome can't be called Nash Equilibrium.
b) if they charge Low price evvery alternate day in 6 weekdays, the profit will be as follows for Kim:
Monday 70
Tuesday 20
Wednesday 70
Thursday 20
Friday 70
Saturday 20
Total Profit of Kim = 270, Average Profit = 270/6 = 45
the profit will be as follows for Harry:
Monday 20
Tuesday 70
Wednesday 20
Thursday 70
Friday 20
Saturday 70
Total Profit of Kim = 270, Average Profit = 270/6 = 45
c) If Kim and Harry decide to randomly charge low price 2/3 days and High Price 1/3 days, we need to calculate the probability of Kim and Harry choosing the different strategy:
2/3 + 1/3 = 3/6 or 1/2 probability that they will chose different strategies
Probability of choosing same price a day = 2/3 + 2/3 = 4/6 or 2/3
So, the Probability of choosing Low price or High Price on the same days can be said 2/3
Which means out of 3 days, there is a probability that Kim & Harry may have profit of 50 each or 10 each.
If profit is 50 each then, total profit of Kim & Harry each may be: 70 + 70 + 70 + 70 + 50 + 50 = 380 / 6 = 63.33 each every day
Or if Both earn a profit of 20 each, then total Profit of Kim & Harry each may be:70 + 70 + 70 + 70 + 20 + 20 = 320 / 6 = 53.33 each every day
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