19.08.2019 ﻿12. Tutorial

doze. 1 Suppose the market for oil is characterized by the need. Suppose you will find two companies, Shell and Caltex. Guess that both firms has a cost of 1 per unit of oil supplied. Assuming symmetry, solve for the following: Allow firm 1 be Caltex, firm a couple of be shell:

12. 1 . 1 Affiliation solution. How much each of the businesses is creating and what is the ensuing price? Exactly what are the firms' profits? If perhaps these two businesses forms a cartel, they can jointly perform like a monopoly.

Profit optimization requires

As a result of symmetry, all the firms is producing

12. 1 ) 2 Competitive market option.

Due to proportion, each of the firms is making

doze. 1 . a few Cournot answer.

Firstly, treat Shell's quantity since given:

(12. )

Pertaining to Caltex to increase its profit, the FOC requires:

(12. )

Subsequently, treat Caltex's quantity since given:

Pertaining to Shell to optimize its profit, the FOC requires:

(12. )

The Cournot-Nash equilibrium is given while:

Market output, market price, and firms' profits are:

12. 1 . 5 Bertrand option.

12. 1 ) 5 Stackelberg solution. Imagine Caltex techniques first and chooses their quantity. Subwoofer Eq. (12. ) into Eq. (12. ):

GENOIS:

Sub in Eq. (12. ) brings:

Hence industry output, market price

12. 1 . six Now imagine Caltex moves first and chooses its price, then simply Shell observes Caltex's selling price and decides about its very own.

doze. 2 Assume now Caltex has the expense of 3, and Shell gets the cost of 1 . 12. 2 . 1 Cournot solution.

1st, treat Shell's quantity while given:

(12. )

For Caltex to increase its income, the GENOIS requires:

(12. )

Second, treat Caltex's quantity because given:

To get Shell to maximize its profit, the GENOIS requires:

(12. )

The Cournot-Nash balance is given because:

Market outcome, market price, and firms' profits are:

12. 2 . 2 Stackelberg remedy. Suppose Caltex moves first and selects its volume.

Sub Eq. (12. )into Eq. (12. ):

FOC:

Sub in Eq. (12. ) brings:

Hence the marketplace output, selling price...