In consideration to the 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, $1$km 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 $$1\mathrm{.}50.$ Unfortunately, there is no way to know whether extra security will be required until after the new checkouts are installed. You have been hired by Alfonso$$s Ammenities to analyse the business case for installing the self$-$service technology. You have been asked to determine: $$ How will self$-$service checkouts affect Alfonso$$s Ammenities profit? $$ Is Bernice$$s Bargains likely to respond by also installing self$-$service checkouts? $$ Should Alfonso$$s Ammenities install the self service checkouts? 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. Step $1$: Derive an expression for the location of the indifferent consumer. Use PA to represent the price of admission at Alfonso$$s Ammenities, and PB to represent the price of admission at Bernice$$s Bargains. Step $2$: Find the profit function for Bernice$$s Bargains. You should assume that Bernice$$s marginal cost is $$15.$ Step $3$: Find Bernice$$s best$-$response function. Step $4$: Find the profit function for Alfonso$$s Ammenities for the case in which their marginal cost is $$12.$ Step $5$: Find the best$-$response function for Alfonso$$s Ammenities for the case in which their marginal cost is $$12$ Step $6$: Find the equilibrium prices and profits for the case in which Alfonso$$s marginal cost is $$12$ and Bernice$$s marginal cost is $$15.$ Step $7$: Find the profit function for Alfonso$$s Ammenities for the case in which their marginal cost is $$13\mathrm{.}50.$ Step $8$: Find the best$-$response function for Alfonso$$s Ammenities for the case in which their marginal cost is $$13\mathrm{.}50.$ Step $9$: Find the equilibrium prices and profits for the case in which Alfonso$$s marginal cost is $$13\mathrm{.}50$ and Bernice$$s marginal cost is $$15.$ please also provide a final conclusion$/$evaluation$/$discussion on the findings and what should be done$/$recommendations