Despondent over the Red Sox's terrible season, Prof. Gruber decides to quit his day job and start a bicycle manufacturing firm in Kendall Square. As he starts looking into the bicycle manufacturing industry, he realizes it has some interesting features. First, he realizes that it operates as a competitive industry. Second, he finds that there are two technologies used by firms in the industry. Technology 1 uses solar power, and has a cost functionC1(q)=q+4q2+32forq>0. Technology 2 uses electricity from the grid and is more efficient, with a cost functionC2(q)=q+2q2+32forq>0. Assume that we are in the long run, so firms using both technologies can shut and leave the market at 0 cost, so thatC(0)=0for both technologies.

Now let's pretend for a minute that only technology 2 exists. Suppose that market demand for bicycles is given byD(p)=82040p. Furthermore, assume that there is free entry for firms using technology 2.

What will be the long-run price in the market? How much will each firm produce at this price? And What will the total number of firms be?