Albert, the rancher, discovers a subterranean cave in his property that has ancient wall paintings which people are willing to pay to see. These viewings can be arranged at a cost of $1 per viewing. The demand for viewing is given by P = 31 - 0.2 Q where P is price in dollars and Q, the number of viewings.
a. What will Albert charge per viewing?
b. Beth, Albert's neighbour, searches her property and finds that there, indeed, is an access to the cave from her property as well.
If both Albert and Beth behave as Cournot duopolists, find their best response curves, outputs and market price.
c. Find their equilibria if they behave as Bertrand duopolists.
d. If Beth behaves as a Stackelberg leader and Albert as a naive Cournot duopolist, find their outputs, profits and price.
e.. If they collude find the market equilibrium.
f. If a third rancher, Colin, also finds access to the cave from his property and if all behave as Cournot oligoplists, find their prices and quantities.
g. In part f. If it cost Beth $2 per view while Albert's cost remains at $1 per view, find the new equilibrium of Albert and Beth if both behave as Cournot oligopolists. What would happen if they are Bertrand Oligopolists?
h. The government also discovers the lucrative nature of the cave paintings and impose a $5 per visit tax. Find the new equilibrium for the data in f. above.