Let’s take a look at Invisible Hand Principle 2 in action using a mathematical example. Suppose an industry is characterized by the equations in the following table. (We’re going to assume all individual firms are identical to make this problem a little simpler.)
Demand ………………………..QD = 100 - 2P
Individual firm’s supply ……….qS = 0.5 + 0.1P
Market supply with n firms …….QS = n × qS = 0.5n + 0.1nP
Individual firm’s average cost ….AC = 5qS - 5 + (24.2/qS)
a. Suppose 24 firms are in this industry. What is the equation for market supply? What is the equilibrium price and quantity (this can be found by setting QD = QS)? How much profit is each firm earning? According to the elimination principle, what should occur in this industry over time?
b. Suppose 35 firms are in this industry. Answer the same questions from part a.
c. The elimination principle says that profits will be eliminated in the long run, which means that AC = P. Using that fact, figure out how many firms will be in this industry in the long run (solve for n).