The inverse demand function for developed land in the city of Kingston is p = 100 0.5Q where Q is the quantity (measured in acres) and p is the price per acre.

(i) Assume for the moment that firm A has the exclusive right to

develop land in the city of Kingston. Then firm A is the monopolist in this

market, and thus Q = qA where qA denotes the number of acres developed by firm

A. Find firm A's output level that would maximize its profit, if firm A's

marginal cost is MCA = 10. Denote this output level by q m A (where the

superscript m indicates that this is the monopoly solution). Compute the

monopoly's profit, and denote it by m A.

(ii) Now assume that the mayor of Kingston allows two firms,

firm A and firm B, to develop land in Kingston. Assume that the two firms

compete as Cournot rivals: the firms set their quantities qA and qB, and the

resulting market price is p = 100 0.5qA 0.5qB. Suppose that the mayor

requires that the two firms choose their output levels simultaneously. Assume

that the marginal cost of firm B is MCB = 10 = MCA. Find each firm's best response

curve. Find their Nash-Cournot equilibrium outputs, and denote them by q C A

and q C B . Find the Nash-Cournot equilibrium price (denoted by p C), and find

the profit of each firm at the Nash-Cournot equilibrium (denoted by C A and

C B).

(iii) Now, suppose that the mayor changes her mind: she allows

firm A to set its qA first (and to announce its output decision) and requires

firm A to make a full commitment to carrying out its announced output decision,

before firm B is allowed to make its choice of qB (having full knowledge of qA

by then). Firm A, being the first mover, is called the Stackelberg leader. Find

the output of the Stackelberg leader, and denote it by q SL A (where the

superscript SL indicates Stackelberg leader). Find the follower's output

(denoting it by q F B , where F stands for "follower"), the industry output,

and the market price under the Nash-Stackelberg equilibrium. Find the

Stackelberg leader's profit, SL A , and the follower's profit, F B .

(iv) Compare q m A (found in part (i) above) and q SL A (found

in part (iii) above). Is it true that q m A = q SL A ? If it is true, can you

tell whether this result is accidental or whether there is some plausible explanation

behind it? Explain your answer.

(v) Now suppose that the mayor allows firm A to be the

Stackelberg leader only if firm A to be the Stackelberg leader only if firm A

pays the mayor a bribe. What is the maximum bribe that the firm A would be willing

to pay. Explain.