1. A profit maximizing monopolist has the following demand and cost functions: P =80–20 TC = Q² +8Q+20 The government is considering imposing an excise tax on the production and sale of the product. The tax increases the variable cost for the firm. For example, if the tax is $2 per unit and the firm produces 10 units then the firm needs to pay $2x10 =$20 total tax to the government. This is added to the firm's cost of production. The government's objective is to generate the maximum possible tax revenue from the monopolist by imposing an excise tax on the production and sale of the product. Drawing a simple diagram describe this as a sequential game. Considering tax rate (t) as the continuous strategy for the government and the output as the continuous strategy for the firm, determine the subgame perfect Nash equilibrium and calculate the optimal tax rate and the optimal level of output. Also, calculate the price charged by the firm. Determine the payoffs in the game when the government's payoff is the tax revenue
1. A profit maximizing monopolist has the following demand and cost functions: P =80–20 TC = Q² +8Q+20 The government is considering imposing an excise tax on the production and sale of the product. The tax increases the variable cost for the firm. For example, if the tax is $2 per unit and the firm produces 10 units then the firm needs to pay $2x10 =$20 total tax to the government. This is added to the firm's cost of production. The government's objective is to generate the maximum possible tax revenue from the monopolist by imposing an excise tax on the production and sale of the product. Drawing a simple diagram describe this as a sequential game. Considering tax rate (t) as the continuous strategy for the government and the output as the continuous strategy for the firm, determine the subgame perfect Nash equilibrium and calculate the optimal tax rate and the optimal level of output. Also, calculate the price charged by the firm. Determine the payoffs in the game when the government's payoff is the tax revenue
Chapter13: Monopoly And Antitrust
Section: Chapter Questions
Problem 7P
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Transcribed Image Text:1. A profit maximizing monopolist has the following demand and cost functions:
P =80– 2Q
TC = Q² +8Q+20
The government is considering imposing an excise tax on the production and sale of the
product. The tax increases the variable cost for the firm. For example, if the tax is $2 per
unit and the firm produces 10 units then the firm needs to pay $2x10 =$20 total tax to the
government. This is added to the firm's cost of production.
The government's objective is to generate the maximum possible tax revenue from the
monopolist by imposing an excise tax on the production and sale of the product.
Drawing a simple diagram describe this as a sequential game. Considering tax rate (t) as
the continuous strategy for the government and the output as the continuous strategy for
the firm, determine the subgame perfect Nash equilibrium and calculate the optimal tax
rate and the optimal level of output. Also, calculate the price charged by the firm.
Determine the payoffs in the game when the government's payoff is the tax revenue
collected and the firm's payoff is the optimal profit (net of all production and tax costs).
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