Alex and Anna are the only sellers of kangaroos in Sydney, Australia. Anna chooses her profit-maximizing number of kangaroos to sell, q1, based on the number of kangaroos that she expects Alex to sell. Alex knows how Anna will react and chooses the number of kangaroos that she herself will sell, q2, after taking this information into account. The inverse demand function for kangaroos is P(q1 +q2) = 2, 000−2(q1 +q2). It costs $400 to raise a kangaroo to sell.
(a) Alex and Anna are Stackelberg competitors. _______ is the leader and _______ is the follower.
(b) If Anna expects Alex to sell q2 kangaroos, what will her own marginal revenue be if she herself sells q1 kangaroos? _______.
(c) What is Anna’s reaction function, _______.
(d) Now if Alex sells q2 kangaroos, what is the total number of kangaroos that will be sold? _______. What will be the market price as a function of q2 only? _______.
(e) What is Alex’s marginal revenue as a function of q2 only? _______. How many kangaroos will Alex sell? _______. How many kangaroos will Anna sell? 200. What will the industry price be? _______.