Competition and the Invisible Hand: End of Chapter Problem _ Let's take a look at Invisible Hand Property 2 in action using a mathematical example. Suppose an industry is characterized by Start by rearranging the individual rm the following equations. We're going to assume that all individual rms are identical to make this problem a little simpler. supply function to get P in terms of '15- I Demand: QB : 100 _ 2P Set that equation equal to the equation | Individual rm's supply: :33 : 0.5 + 0.] P for AC and SOIVC for (1;. | Market supply with n rms: Q5 : n X :15 : 0.5): + DJnP | Individual rm's average cost: AC : Sag 5 + Mf e. The Elimination Principle says that prots will be eliminated in the long run. which means that AC 2 P. We will use that fact to gure out how many rms will be in this industry in the long run. Using AC : P, nd gs, the number of units that each firm Will make in the long run. I Q'S- Then use qs to nd P, the longrun price of output. Now use P to nd (23, the amount of output demanded by ' th 1 I . Finally, use Q3 and (159 to nd It, the number of rms in the