Question

c) Consider a city which is locate on a long (10 km.) thin island. It has a population density of 100 people per km. which is the same everywhere in the city. Each person drinks exactly 1 cup of coffee per day and are willing to pay $5 per cup. The average cost of selling coffee is simple: the minimum average cost is $2 per cup if it sells 200 cups per day and the average cost rises by 10 cents for every 10 cups more or less than this amount (i.e. one each side of the minimum, the AC curve is a straight line where, for example, the average cost of selling a cup of coffee would equal $3 if it sold 100 cups per day and the average cost would be $4 if it sold 400 cups per day.

            i) How many sellers would there be in this city, in equilibrium?

            ii) Where the sellers would locate in equilibrium? For a marginal consumer in that equilibrium, how much benefit do they enjoy, in dollar terms relative to the situation of having only one store in town and the price did not change from that in a)?

Answer 1

So let's talk about what we know. There are 100 people per km on a 10 km wide, thin island. This means there are 1,000 people on the island.

Everyone drinks coffee every day. The maximum Willingness to Pay (WTP) per consumer is $5. So we know that there is $5,000 worth of revenue made per day selling coffee on the island.

Now let's talk about costs. Basically, for every 100 cups of coffee sold the variable cost per cup of coffee increases by $1. So right off the bat we know that we need to have more than 2 coffee sellers on the island. This is because if there were only 2 then those two would be selling 500 cups each at a cost of $5 each so there would be no profit in that. (btw I'm assuming that the number of cups sold is evenly distributed between competitors).

The prompt states that 200 cups costs $2 per cup so we know we are going to want to be somewhere near that to minimize our costs. So if there are 4 sellers in the market, that means the cost per cup would be $2.50. This means profit per cup would be $2.50 and with 250 units sold the profit per competitor would be $625. Now let's say there are 5 competitors @ a cost of $2.00 per cup and 200 cups sold by each competitor. $3 in profit x 200 cups only equals $600. So we know that there will only be 4 competitors in the market to maximize profits in this equilibirium.

Now for the 2nd part. What would make the most sense is this situation is to space every seller equidistance away from one another to ensure all consumers are covered. We know the island is 10 km wide and thin so each seller should be 2.5 miles away from one another. The only way to make this work fairly though is to work from one end of the island to the other and spacing the sellers appropritately. So Seller1 would be set up 1.25 km away from the edge of the island, and then seller 2 would be set up 2.5 km away (this gives both sellers 2.5 kms of territory in total with 1.25 km on either side of their shop). This continues on for seller 3 and 4.

The average consumer would benefit greatly from this. Instead of consumers on the periphery having to walk up to 5 km to get to the 1 seller in town (presumably in the middle), they are never farther than 1.25 km from a seller.

Now in terms of the benefit they receive in terms of dollars, that I'm not 100% certain on in terms of this question. The question doesn't pose anything related to consumers in terms of dollar amounts such as time spent having to travel to get the coffee or opportunity cost, etc. It feels like there is information missing here that I would need to answer the question. Unfortunately, I can only guess at this point which won't do you any good.

My suggestion is refer to other information you have regarding this question or ask for clarification from your professor. Remember that the marginal consumer only has to travel 1.25 km at most now, unlike before where if there was only 1 seller on the island on one end they could potentially have to travel up to 10km to get their coffee and another 10 km to return home. Hopefully there exists information to help quantify the benefit they receive.