Kendall Square Inc makes and sells ramen to the large number of students around MIT. Kendall Square Inc uses the production function

(,)=(+2)1/3 (raised to power of 1/3)

Input prices are=2 and=3 for labor and capital respectively. It operates in a perfectly competitive environment facing a price=$48 , and uses an initial amount of capital =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 market demand is given by()=9720/

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

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.

What will be the long-run equilibrium price in the market?

= ?

At that price, how much will each firm produce?

= ?

What is the total number of firms in the market in the long run?

= ?

If the manager of Kendall Square, Inc works hard, she can manage to transform the long-run cost function you derived in PS5.3.5 by cutting Kendall Square Inc's variable costs in half. That is, she can halve the part of the long-run cost function unrelated to her fixed wage of$54

. Suppose that the rest of the market doesn't change: the other firms can only hire mediocre managers who cannot cut the cost functions and so the long-run market price remains fixed at the same level you calculated earlier.

What is the new optimal long-run production level for Kendall Square, Inc?

= ?

What are the new long-run profits for Kendall Square, Inc?

= ?

Instead of working hard, Kendall Square Inc's manager can shirk and not improve costs. In order to incentivize her hard work, Kendall Square Inc's shareholders want to give the manager a bonus if they see that variable costs are cut by half.

What is the maximum bonus that shareholders would be willing to give?