Scenario: In the town of Isoville there are two grocery stores: Alfonso’s Ammenities and Bernice’s Bargains. The grocery stores are located at either end of the town, 1km apart. Recently, the manager of Alfonso’s Ammenities has proposed installing new self-service checkout technology, which promises to reduce the cost of each transaction at the grocery store by reducing staffing costs. The new technology is expected to reduce the marginal cost of selling a typical basket of groceries by $3. However, experience in other locations has shown that in about 25% of installations the self-service technology results in a significant increase in shop-lifting. In these cases, the need to hire extra security staff means that the marginal cost of a typical basket only falls by $1.50. Unfortunately, there is no way to know whether extra security will be required until after the new checkouts are installed.
Scenario: In the town of Isoville there are two grocery stores: Alfonso’s Ammenities and Bernice’s Bargains. The grocery stores are located at either end of the town, 1km apart. Recently, the manager of Alfonso’s Ammenities has proposed installing new self-service checkout technology, which promises to reduce the cost of each transaction at the grocery store by reducing staffing costs. The new technology is expected to reduce the marginal cost of selling a typical basket of groceries by $3. However, experience in other locations has shown that in about 25% of installations the self-service technology results in a significant increase in shop-lifting. In these cases, the need to hire extra security staff means that the marginal cost of a typical basket only falls by $1.50. Unfortunately, there is no way to know whether extra security will be required until after the new checkouts are installed.
The Market: Isoville has 12,000 households, each of which purchases 1 basket of groceries per week. The households are evenly spaced across the town and they each suffer a disutility of $4 for each kilometre they travel to reach a grocery store.The marginal cost of selling a basket of groceries is currently $15 for each store. At present, the
This market is best modelled as Hotelling competition. You should neglect fixed costs in your analysis. (Assume that the fixed costs are the same for both types of checkout technology.)
Note: For the purposes of this assignment you should treat competition in this market as a one-shot game. Do not consider repetition or associated phenomena such as collusion or predatory pricing.
Step 7: Find the profit function for Alfonso’s Ammenities for the case in which their marginal cost is $13.50.
Step 8: Find the best-response function for Alfonso’s Ammenities for the case in which their marginal cost is $13.50.
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