Scenario

In the town of Isoville there are two grocery stores: Alfonsos Ammenities and Bernices Bargains. The grocery stores are located at either end of the town, 1km apart.

Recently, the manager of Alfonsos 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.

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 equilibrium price a basket of groceries is $19, and each store has a profit of $24,000 per week.

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.

Task

You have been hired by Alfonsos Ammenities to analyse the business case for installing the self-service technology. You have been asked to determine:

How will self-service checkouts affect Alfonsos Ammenities profit?

Is Bernices Bargains likely to respond by also installing self-service checkouts?

Should Alfonsos Ammenities install the self service checkouts?

Write a report according to the following structure:

1. Introduction

Summarize the purpose of the report.

Outline the methodology employed, and key findings

2. Analysis

Step 1: Derive an expression for the location of the indifferent consumer. Use PA to represent the price of admission at Alfonsos Ammenities, and PB to represent the price of admission at Bernices Bargains.

Step 2: Find the profit function for Bernices Bargains. You should assume that Bernices marginal cost is $15.

Step 3: Find Bernices best-response function.

Step 4: Find the profit function for Alfonsos Ammenities for the case in which their marginal cost is $12.

Step 5: Find the best-response function for Alfonsos Ammenities for the case in which their marginal cost is $12.

Step 6: Find the equilibrium prices and profits for the case in which Alfonsos marginal cost is $12 and Bernices marginal cost is $15.

Step 7: Find the profit function for Alfonsos Ammenities for the case in which their marginal cost is $13.50.

Step 8: Find the best-response function for Alfonsos Ammenities for the case in which their marginal cost is $13.50.

Step 9: Find the equilibrium prices and profits for the case in which Alfonsos marginal cost is $13.50 and Bernices marginal cost is $15.

1. Discussion

In your discussion you should address all the issues raised in the scenario. This includes explaining the significance of the findings of your analysis in the context of the scenario, and providing arguments in support of the conclusions of your report. Be sure to base your discussion on the results in your analysis section and avoid assertions or speculation. Use economic terminology as appropriate.