Suppose there are n cities producing n different goods,

Suppose there are n cities producing n different goods, which they each trade with the other n-1 cities. We will normalize the quantity of goods shipped from each city to each of the other cities to be one. The cost of shipping between any two cities is $ xo.5, where x is the quantity of goods in a given shipment. Direct shipments involve only one unit of goods. If a new trading city with no produced goods is created to serve as a trading hub, then all n units of each good produced in each of the original cities can be combined in one shipment to the trading city and then rebundled with one unit of the n-1 other goods for shipment from the trading city to the n other cities. Write down an expression for the total cost of all direct shipments as a function of the number of cities. Now do the same for the cost of shipment through the hub. For n=3, 4, 5, 6, 7, 8, 9, and 10, plot the cost of direct shipping and indirect shipping. Now comment on the following statement, “Hub City does not produce anything and does not contribute to the economy.”