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

Now suppose that the State of Massachusetts increases the number of solar bike manufacturing subsidies it will give 100. These subsidies are for $80 and the manufacturers receive these subsidies as long as they construct a bicycle manufacturing plant using the newly-invented solar technology (i.e. technology 1).

Calculate the following -

What is the new long-run price?

How much will be produced in total by firms with technology 1?

How much will be produced by total by firms with technology 2?

How many firms will there be with technology 1?

How many firms will there be with technology 2?

How much profit will be earned by each firm with technology 1?

How much profit will be earned by each firm with technology 2?