Exam 7: Static Games With Continuous Strategies

Suppose that the land surrounding a lake is owned by individuals A andB. Both individuals use the lake to earn a living from fishing, where f_A and f_B represent the total amount of fish extracted from the lake from the two individuals. The benefit from each fish is $200 ! f_A !f_B. The marginal cost of fishing for each profit-maximizing individual is $50. What is total fish production?

Suppose that the land surrounding a lake is owned by individuals A andB. Both individuals use the lake to earn a living from fishing, where f_A and f_B represent the total amount of fish extracted from the lake from the two individuals. The benefit from each fish is $200 ! f_A !f_B. The marginal cost of fishing for each profit-maximizing individual is $50. How many fish will individual B catch?

Suppose that the land surrounding a lake is owned by individuals A andB. Both individuals use the lake to earn a living from fishing, where f_A and f_B represent the total amount of fish extracted from the lake from the two individuals. The benefit from each fish is $50 ! f_A !f_B. The marginal cost of fishing for each profit-maximizing individual is $20. How many fish will individual A catch?

Suppose that an industry consists of two firms producing an identical product. The market demand for the combined output of both firms is (Q_A + Q_B) = 50 !P. The total cost function of each firm is TC_i = 1 + 10Q_i, where i = A,B. Firm B's best-response function is:

An industry consists of two firms producing identical goods. The market demand for the combined output of both firms is (Q_A + Q_B) = 100 !0.2P. The total cost function of each firm is TC_i = 100 + 200Q_i, where i = A,B. Firm A's best-response function is:

Suppose that the land surrounding a lake is owned by individuals A andB. Both individuals use the lake to earn a living from fishing, where f_A and f_B represent the total amount of fish extracted from the lake from the two individuals. The benefit from each fish is $200 ! f_A !f_B. The marginal cost of fishing for each profit-maximizing individual is $50. How many fish will maximize social welfare?

The "tragedy of the commons":

To achieve a socially efficient level of output, government should impose a pollution tax that is equal to:

Suppose that the land surrounding a lake is owned by individuals A andB. Both individuals use the lake to earn a living from fishing, where f_A and f_B represent the total amount of fish extracted from the lake from the two individuals. The benefit from each fish is $200 ! f_A !f_B. The marginal cost of fishing for each profit-maximizing individual is $50. How many fish will benefit-maximizing individual A catch?

Suppose that an industry consists of two firms producing an identical product. The market demand for the combined output of both firms is (Q_A + Q_B) = 50 !P. The total cost function of each firm is TC_i = 1 + 10Q_i, where i = A,B. Firm A's best-response function is:

An industry consists of two firms producing identical goods. The market demand for the combined output of both firms is (Q_A + Q_B) = 100 !0.2P. The total cost function of each firm is TC_i = 100 + 200Q_i, where i = A,B. Firm B's best-response function is:

An industry consists of two firms producing identical goods. The market demand for the combined output of both firms is (Q_A + Q_B) = 500 !0.5P. The total cost function of each firm is TC_i = 250 + 50Q_i, where i = A,B. The Nash equilibrium strategy profile for this game is:

A reaction function is also called a:

In the case of a negative externality, social marginal cost:

An industry consists of two firms producing identical goods. The market demand for the combined output of both firms is (Q_A + Q_B) = 100 !0.2P. The total cost function of each firm is TC_i = 100 + 200Q_i, where i = A,B. The Nash equilibrium strategy profile for this game is:

Suppose that the land surrounding a lake is owned by individuals A andB. Both individuals use the lake to earn a living from fishing, where f_A and f_B represent the total amount of fish extracted from the lake from the two individuals. The benefit from each fish is $50 ! f_A !f_B. The marginal cost of fishing for each profit-maximizing individual is $20. How many fish will individual B catch?

A perfectly competitive chemical plant dumps large amounts of waste into a nearby river. From society's perspective, the chemical plant:

Suppose that the best-response pricing functions for firms A and B are P_A = 0.22 + 0.5P_B and P_B = 0.10 + 0.2P_A, respectively. The Nash equilibrium strategy profile for this static game with continuous strategies is:

An industry consists of two firms producing identical goods. The market demand for the combined output of both firms is (Q_A + Q_B) = 500 !0.5P. The total cost function of each firm is TC_i = 250 + 50Q_i, where i = A,B. Firm B's best-response function is:

Suppose that the land surrounding a lake is owned by individuals A andB. Both individuals use the lake to earn a living from fishing, where f_A and f_B represent the total amount of fish extracted from the lake from the two individuals. The benefit from each fish is $50 ! f_A !f_B. The marginal cost of fishing for each profit-maximizing individual is $20. What is total fish production?