Now suppose that, in addition to its existing capital and labor inputs, Kendall Square, Inc must hire a manager for a fixed amount of$54in 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 byD(p)=9720p. 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?

p=

At that price, how much will each firm produce?

q=

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

N=

2.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 in PS5.3.5.

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

q=

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?.......................................

3.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.

Compute the marginal cost for technology 1.

MC1(q)=

A. 1+8q

B. None of the above

C. 1+2q+32q

D. 1+4q+32q

E. 1+4q

Compute the marginal cost for technology 2.

MC2(q)=

A. 1+4q

B. None of the above

C. 1+4q+32q

D. 1+8q

E. 1+2q+32q

Compute the average cost for technology 1.

AC1(q)=

A. 1+8q

B. 1+4q+32q

C. 1+2q+32q

D. None of the above

E. 1+4q

Compute the average cost for technology 2.

AC2(q)=

A. None of the above

B. 1+2q+32q

C. 1+8q

D. 1+4q

E. 1+4q+32q

4.Derive the supply curve for each technology.

q1(p)=

A. 1p/8

B. None of the above

C. p1/4

D. p1/8

E. 1p/4

q2(p)=

A. 1p/4

B. None of the above

C. p1/8

D. 1p/8

E. p1/4