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2.a Show that if Firm E does not update its belief, its optimal choice is entering this market. Next, we investigate if Firm I is low-cost (c = 0), whether it can signal Firm E this information by setting a particular level of p1.

2.a Show that if Firm E does not update its belief, its optimal choice is entering this market. Next, we investigate if Firm I is low-cost (c = 0), whether it can signal Firm E this information by setting a particular level of p1.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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2.a Show that if Firm E does not update its belief, its optimal choice is entering this market. Next, we investigate if Firm I is low-cost (c = 0), whether it can signal Firm E this information by setting a particular level of p1.
Transcribed Image Text:2.a Show that if Firm E does not update its belief, its optimal choice is entering this market. Next, we investigate if Firm I is low-cost (c = 0), whether it can signal Firm E this information by setting a particular level of p1.
Suppose there is only 1 consumer who has a demand of a product up to 1 unit per period. There are 2 periods. Her willingness to pay is S10 per unit. There are two firms, I and E. Firm I is the incumbent and is the only producer in the 1" period. Firm E is the potential entrant with 0 marginal cost but must incur an entry cost of $1 if entering this market. Firm I knows its marginal cost (c) but Firm E does not know for sure: it knows c is either 0 or 5. Without any further information/signal, Firm E believes the probability for either case is 50%. The timing of the game is the following: • Firm I sets the price in the 1ª" period (pi); • Firm E makes its entry decision; • Were “not enter" chosen, Firm I will remain as a monopoly in the 2nd period and set the price at $10. • Were "enter" chosen, the two firms engage in Bertrand competition in the 2nd period. Lastly, assume both firms have a discount factor of 0.8.
Transcribed Image Text:Suppose there is only 1 consumer who has a demand of a product up to 1 unit per period. There are 2 periods. Her willingness to pay is S10 per unit. There are two firms, I and E. Firm I is the incumbent and is the only producer in the 1" period. Firm E is the potential entrant with 0 marginal cost but must incur an entry cost of $1 if entering this market. Firm I knows its marginal cost (c) but Firm E does not know for sure: it knows c is either 0 or 5. Without any further information/signal, Firm E believes the probability for either case is 50%. The timing of the game is the following: • Firm I sets the price in the 1ª" period (pi); • Firm E makes its entry decision; • Were “not enter" chosen, Firm I will remain as a monopoly in the 2nd period and set the price at $10. • Were "enter" chosen, the two firms engage in Bertrand competition in the 2nd period. Lastly, assume both firms have a discount factor of 0.8.
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