Find the Stackelberg equilibrium and compare it to the Cournot equilibrium.

6. Demand and costs are as given in the preceding question.

(a) Find the limit output for fixed costs ( f ) equal to 50, 32, 18, and 2.

(b) What is the SPNE for the entry game with the following timing: in the first-stage firm 1 can commit to its output; in the second stage firm 2 can enter and choose its output for fixed costs equal to 50, 32, 18, and 2?

Thank you.

Solution Preview

5.

For simplicity, I will use x for the output of firm 1 (i.e q1) and y for the output of firm 2 (i.e. q2).

The inverse demand function, in terms of x and y, is P = 56 - 2x - 2y

The cost functions for each firm is C1 = 20x + f and C2 = 20y + f

The profit of firm 1 = x(56 - 2x - 2y) - 20x - f and the profit of firm 2 = y(56 - 2x - 2y) - 20y - f.

Expanding the brackets gives profit 1 = 56x - 2x^2 - 2xy - 20x - f and profit 2 = 56y - 2xy - 2y^2 - 20y - f.

Differentiating and setting to zero gives

56 - 4x - 2y - 20 = 0
56 - 4y ...

Solution Summary

The stackelberg equilibrium and SPNE are provided. Cost functions for inverse demands are analyzed.

I have changed the values and need the model to plug my numbers in.
Please solve with explanations.
1. The inverse demand curve for a Stackelberg duopoly is
P = 5,000 - 3Q.
The leader's cost structure is
CL(QL) = 1250 + 10QL.
The follower's cost structure is
CF(QF) = 250 + 20QF.
a. Determine the reaction fu

11. The inverse demand curve for a Stackelberg duopoly is . The leader's cost structure is . The follower's cost structure is .
a. Determine the reaction function for the follower.
b. Determine the equilibrium output levels for both the leader and the follower.
c. What are the profits for the leader? For the follower?

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1. Consider the following market demand and asymmetric cost functions for the airplane production industry.
Market Demand is: P=200- (qA + qB)
Cost Function for Boeing: C(qB) = 40 qB
Cost Function for Airbus: C(qA) = 30 qA
a.) Assume that the two act according to the Cournot mo

1. The industry demand function facing two oligopolists is p = 100 - 0.5y1 - 0.5y2, where yi is the production of firm i, and p is the price of their homogeneous output. Each firm has a cost function of the form ci = 10yi
(a) Calculate the Cournot level of output for each firm.
(b) Calculate the output for each firm when fir

H T
H -1,1 1,-1
T 1,-1 -1,1
1. What is the MSNE of the matching pennies game above?
2. Make a graph of the best-responses.
3. Suppose this game were repeated 15 times. What would be the SPNE of the repeated game?
Suppose that someone decided to hold the World Series of Matching Pennies in Las Vegas, Nevada. The contes

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Consider the following gas-phase equilibrium reaction:
N2(g) + 02(g) <-- (double arrow for equilibrium) --> 2NO(g)
Kc = 4.10 X 10 ^-4 at 2000 Degrees Celsius.
If 1.0 mol of NO is introduced into a 1.0 L container at 2000 Degrees Celsius, what is the concentration of NO when equilibrium is reached.