please help and show full calculations Two firms are considering the introductio

Question

please help and show full calculations

Two firms are considering the introduction of new brands of roller-blade skates. The payoff matrix is as follows: Does this game have any Nash equilibrium? Explain. Suppose the market for semiconductors is characterized by the following information: Qd = 70-5P [Demand] Qs = 3P-10 [Supply] Calculate the deadweight loss (DWL) due to a sales tax of $2 per semiconductor.[Note: P = price per semiconductor; Qd = thousands of semiconductors demanded; Qs = thousands of semiconductors supplied]

Explanation / Answer

A) In the given game, If Firm 2 choses to play 'Introduce', it will be benefical for Firm 1 to chose 'Dont Introduce'. If Firm 2 choses to play 'Dont Introduce', it will be benefical for Firm 1 to chose 'Introduce'. Likewise for Firm 1.

Thus, there is no Nash equilibrium in the game as neither of the players have any dominant strategies, and at every move, either of the players will have an incentive to deviate.

B) Qd = 70-5P and Qs = 3P-10

Equilibrium will be where Qd = Qs

This will be where P = $10 and Q = 20

With imposition of sales tax, demand curve remains the same

Supply curve (new) becomes: P = (Qs+10)/3 + 2Q

New equilibrium will be where Qd = Qs

This gives equilibrium values as: New P = $13 and Q = 4 (approx.)

Dead weight loss = Area of triangle = (1/2)*(13-10)*(20-4) = 24

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