Monopoly and Oligopoly
1.Third-degree price discrimination
S钞票的英文ince the market is parated into two groups, submarket, then we face two demand functions, and. Thus, profit maximization problem can be described as
Hence, FOC is
, and
Other situation: combination of the two parated markets
Horizontal summation:
Optimal solution:
2.Oligopoly behavior
A.Cournot model —— Simultaneously quantity tting
Conditions: market demand, products are identical, marginal cost of the two firms are equal and constant,, they decide their output decision simultaneously without knowing other’s decision advanced.
Maximization problem:
s.t.
s.t.
Solution:
(1)Since , then, its FOC is shown as
, after rearranging, this yields the reaction function of firm 1,
(2)The same, we have the reaction function of firm 2
(3)Combine the two reaction functions, we have
B.Bertrand model —— Simultaneously price tting
C.Stackelberg model (quantity leadership model)
Conditions: market demand, products are identical, marginal cost of the two firms are equal and constant,, however, firm 1 is quantity leader, who makes his output decision first, firm 2 is follower, who makes his decision with knowing firm 1’s decision.
Maximization problem:
s.t. & firm 2’s reaction function
s.t.
Solution: backward induction
(1) Since, thus,
, hence, firm 2’s reaction function is
(2) And , substitute firm 2’s reaction function, then
Iso-profit curves can be shown as
thus, optimal choice appears when
S裸购o that
D.Price leadership model
Conditions: market demand, products are identical, marginal cost of the two firms are, however, firm 1 is price leader, who makes his pricing decision first, firm 2 is follower, who makes his decision with knowing firm 1’s decision.
femaleTraditional Method:我想学英语
Taking u of backward induction:
Maximization problems of follower
FOC:
Thus, the reaction function of follow is , in other words, it’s supply function of the follower.
Then we consider the maximization problem of price leader
s.t.
Substituting into the above constraint, then,
, more generally, , which is residual demand for firm 1.
Then the maximization problem becomes
Thus, FOC is
Hence,, then , and then
Comparison: Stackelberg model VS. Price leadership model
Here, we try to make a comparison between stackelberg model and price leadership model, focusing on the esntial difference with respond to solution process and outcome.
Conditions of economic situation；
market demand, products are identical, marginal cost of the two firms are, however, firm 1 is decision leader, who makes his decision first, firm 2 is follower, who makes his decision with knowing firm 1’s decision.
Ca (1): Stackelberg model
Solution:eitheror
a. Follower’s Maximization problem with knowing firm1’s output quantity decision
s.t.
Thus, FOC is
Hence, the respond function of firm 2 is
hkexb. Leader’s Maximization problem with expecting firm2’emtos responds
s.t.
& firm 2’s reaction function
Substituting all constraints into maximization problem, this yields
Thus, FOC is
Hence, ,
c. Equilibrium
Ca (2): 半轴漏油Price Leadership model
Solution:
a. Follower’s Maximization problem, knowing firm1’s output quantity and price decision
s.t.
emitAt this time, there are two rules that we don’t know whether it is matched.
FOC: , or
Hthereafterence, there are two probable reaction functions.
, or
If both of the above reaction functions are equivalent, then
, that is firm 1’s residual demand:
b. Leader’s Maximization problem with expecting firm2’s responds
