endall Square Inc makes and sells ramen to the large number of students around MIT. Kendall Square Inc uses the production function F(K,L)=(K+2L)1/3. Input prices are w=2 and r=3 for labor and capital respectively. It operates in a perfectly competitive environment facing a price p=$48, and uses an initial amount of capital K^=12.

Now suppose that, in addition to its existing capital and labor inputs, Kendall Square, Inc must hire a manager for a fixed amount of $54 in order to function properly. Suppose that all firms have the same long-run cost function as Kendall Square, Inc (they must also hire a similar manager), and the 11 market demand is given by D(p)=9720/p. Suppose there are 59 other identical firms in the market (i.e. 60 identical firms in total) and no entry or exit due to government regulation.

5. What is the firm's profit?

For the rest of the problem, assume that we are in the long run with free entry in the market.

6. What will be the long-run equilibrium price in the market?p=

7. At that price, how much will each firm produce?q=

8. What is the total number of firms in the market in the long run?N=