4 45 points Assume that Hualien consists of a single circle

4. (45 points) Assume that Hualien consists of a single circle street that is L mile long and has N residents uniformly located on it. There are 3 independent video rental stores evenly located on the circle street. Each resident rents one video per day provided that the price charged is no more than Sv. The unit transportation cost is t. Suppose first that the stores are unable to price discriminate. m stands for price firm i charges, i-1,2,3. (a) What prices will the three stores set given that they act as price competitors (10 points) (b) What profits do they earn? (5 points) (c) Now suppose firm 1 and firm 2 merge without changing their locations. What (d) Based your answer in part (c), how do you intuitively explain the ranking of the (e) Comparing your answers in part (c) with part (a), how do you intuitively explain are the post-merger prices? (5 points) post-merger prices? (5 points) the change in the post-merger prices? (5 points) Assume now firms can practice perfect price discrimination. diagram we discussed in class to compare the profits before and after merger to (f) Do firm 1 and firm 2 still have an incentive to merge? (Hint: employ the answer this question.) (10 points) (g) How does such merger affect the price of the nonmerged firm charge? (No calculations needed. Provide an intuitive interpretation.) (5 points)

Solution

Circle Street having 3miles circumference with 3 stores evenly located. Each resident rents one video per day paying no more than $V (Max Price). There is a cost of transportation involved for the store owners i.e. ‘t’. Without price discrimination, Price= m per unit i. where i= 1, 2, 3. Competitive price setting is based on the price the other competition is charging. As all the video rental stores are evenly located and have a similar product. A completion based pricing strategy involved setting price based on competitor’s price rather than on your own costs and profit objectives. The price war that will be led by the competitors will make the price minimum. Each firm will try to charge the minimum price they can to win this price war. If the difference in the price is going to be very low between the competitors, the distance travelled by the person to the store might play a major role. A market-controlled environment shows a higher level of competition with similar products and little price control by individual companies. Every product has a price range. To decide where you fit on the current price range of your competitors or if you should choose something outside it, compare your product to those of your competitors. As people will prefer renting from their nearest store as they will save their time travelling to the store that is far away from their place. If travelling is ignored than the price charged by the store owners will be Min ($V) - $t = Profit. If there is no price war and people prefer to buy from the nearest store than the price will be m. A key component to pricing your product right is to continuously monitor your prices and those of your competitors. When the prices of all the competitors are equal than the price = m and the profit margin will be $m - $t = Profit But if the price discrimination exist than the store owners would rather choose to lower their price so that they can attract more customers. Here travelling time to the store might play a major role leading some of the customers living near to the other store may choose to rent the video from the nearest store because of marginal difference in price. If there exists a price discrimination, the profit margin for all the store owners will go very low and can result in store owners exiting the market. The best strategy for the store owners is to set the price to m and no discriminate in price. Else the profit will be Min ($V) - $t = Profit. There will be no change in prices with the merger. As there still exists a competition in the market that is the third store. If any of the store owner starts the price war people will shift towards the store charging the lesser price. But the merged store can play a vital role for the people who are living near them. They can charge a very less profit margin that hardly affects them and can earn some extra profit. The prices will therefore remain unchanged. It will be best for all the store owners to set the same price that will lead to higher profit for all stores as the transportation cost for a unit is same for all stores. The prices will remain unchanged and will only change if all the stores cooperate together. Store owners will have to reach the end of the price war that maximizes the profit for each store as even after the merger the prices cannot be changed. The price discrimination will lead to short run profit and higher expectation of customers for that price. The market segmentation approach can build loyalty and see customers progress to higher price points as their circumstances and needs change. Customers use the existing prices as a guide to what is normal or considered a good deal, so be prepared to handle the consequences of pricing outside the standard range by selling value. This leads to competitors changing the good rather than staying on the same good forever. The best approach for all the store owners is to set a distinctive price and earn high profit that is spread all over the stores. It will be convenient for the customers and the store owners as a whole leading to social benefits and profits.