Please provide all working. Questions are attached.
The inverse demand function for developed land in the city of Kingston is p = 100 0.56.2 where Q is the quantity (measured in acres) and p is the price per acre. ('1) (iii) (1") Assume for the moment that rm A has the exclusive right to develop land in the city of Kingston. Then rm A is the monopolist in this market, and thus Q = (154 where (M denotes the number of acres developed by rm A. Find rm A's output level that would maximize its prot, if rm A's marginal cost is M 0,4 = 10. Denote this output level by q' (where the superscript m indicates that this is the monopoly solution). Compute the monopoly's prot, and denote it by 1T3}. (3 marks.) Now assume that the mayor of Kingston allows two rms, rm A and rm B, to develop land in Kingston. Assume that the two rms compete as Cournot rivals: the rms set their quantities (1,4 and qg, and the resulting market price is p = 100 0.5% 0.5193. Suppose that the mayor requires that the two rms choose their output levels simultaneously. Assume that the marginal cost of rm B is M03 = 10 = MCA. Find each rm's best- response curve. Find their Nash-Cournot equilibrium outputs, and denote them by qg and qg. Find the Nash-Cournot equilibrium price (denoted by p0), and nd the prot of each rm at the Nash-Cournot equilibrium (denoted by \"HE and g). (5 marks.) Now, suppose that the mayor changes her mind: she allows rm A to set its (1,; rst (and to announce its output decision) and requires rm A to make a full commitment to carrying out its announced output decision, before rm B is allowed to make its choice of (LB (having full knowledge of (M by then). Firm A, being the rst mover, is called the Stackelberg leader. Find the output of the Stackelberg leader, and denote it by qf' (where the superscript SL indicates Stackelberg leader). Find the follower's output (denoting it by qg, where F stands for \"follower\"), the industry output, and the market price under the Nash-Stackelberg equilibrium. Find the Stackelberg leader's prot, \"REL, and the follower's prot, 3?. (6 marks.) Compare q? (found in part (i) above) and qiL (found in part (iii) above). Is it true that q\" = qf'? If it is true, can you tell whether this result is accidental or whether there is some plausible explanation behind it? Explain your answer (maximum length: 50 words). (3 marks.) Now suppose that the mayor allows rm A to be the Stackelberg leader only if rm A pays the mayor a bribe. What is the maximum bribe that rm A would be willing to pay? Explain your answer (maximum length: 100 words). (3 marks.)
