Purchase Solution

Stackelberg Equilibrium & SPNE

Not what you're looking for?

Ask Custom Question

Please help me with the following:

5. Suppose that inverse demand is given by

D(Q) = 56 − 2Q, Q = q1 + q2

and the cost function is

TC(qi ) = 20qi + f

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.

Purchase this Solution

Solution Summary

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

Solution Preview


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 ...

Purchase this Solution

Free BrainMass Quizzes
Economic Issues and Concepts

This quiz provides a review of the basic microeconomic concepts. Students can test their understanding of major economic issues.

Economics, Basic Concepts, Demand-Supply-Equilibrium

The quiz tests the basic concepts of demand, supply, and equilibrium in a free market.

Basics of Economics

Quiz will help you to review some basics of microeconomics and macroeconomics which are often not understood.

Pricing Strategies

Discussion about various pricing techniques of profit-seeking firms.

Elementary Microeconomics

This quiz reviews the basic concept of supply and demand analysis.