Consider the following demand P=72-Q. Assume that there are two producers with i
ID: 1096720 • Letter: C
Question
Consider the following demand P=72-Q. Assume that there are two producers with identical costs functions of the form C(Q) = 4Q. Imagine that one firm is in a privileged position acts as a leader the other firm observes the actions of the first firm and then takes an action with regard to quantity produced. i) Find the total quantity supplied and the equilibrium price. ii)Which firm makes higher profits? iii)Is the combined profit higher than the one that would be earned by two firms competing a'la Cournot?Explanation / Answer
i) P = 72 -Q
C(Q) = 4Q
Differentiating cost function;
MC = 4
Leader output = a-MC/2b
=72 -4/2
= 34
Follower output = a-MC/4b
= 68/4
= 17
total output = 34+17
= 51
Equilibrium Price = 72 - 51
= $ 21
ii) Profit of Leader = 34*21 -4*34
= 714-136
=$578
Profit of follower = 17*21 -4*17
=357-68
=$289
Leader earns more profit
iii) Output in the Cournot
P = 72-Q
C(Q) =4Q
This is the case of Duopoly
On differentiating the Cost function (4Q)
MC = 4
Equilibrium in Competitive market
P = MC
72-Q = 4
Q = 68
Duopoly Quantity = N/N+1 *Competitive quantity
Q=2/3*68
= 45.33
Substitute it in the demand function:
P = 72-45.33
=$26.33
Profit in Cournot = 45.33*26.33 - 4*45.33
=1,193.53 -181.32
=$1012.21
Profit in Cournot Market is higher than the Stackelberg