Section II: Game theoretic approach toward analyzing output behavior of rivals (50 points)
Firms X and Y are duopolists facing the same two strategy choices. They can either tacitly collude or they can compete in a Cournot fashion. The market demand for their product, as well as their respective cost curves are as follows:
C(qx) = C(qy) =50qi (firm X and Y’s total cost curves), where i=x or y
MC(qy) =MC(qy) = 50 (firm X and Y’s marginal cost curves)
P=500-5Q, (market demand), where Q = qx + qy .
C(q) and have the same cost structure: marginal cost and average cost both=50
a.) Calculate the respective output levels of each firm if they collude to set monopoly prices.
b.) Calculate the respective output levels of each firm if they adhere to the Cournot model.
c.) What four possible output combinations are available in this game?
d.) Derive the for possible profit outcomes for each firm that arise from producing the four possible output combinations available in this game.
e.) Use these profit outcomes to construct a 2×2 normal representative matrix for this game.
f.) Does either firm have a dominant strategy? If so, what is it?
g.) Is there a Nash equilibrium for this game? If so, what is it?
h.) Is the outcome of this game a prisoner’s dilemma? Please Explain?
Please show all work to receive full credit.
Firms X and Y are duopolists facing the same two strategy choices. They can either tacitly collude or they can compete in a Cournot fashion. The market demand for their product, as well as their respective cost curves are as follows:
C(qx) = C(qy) =50qi (firm X and Y’s total cost curves), where i=x or y
MC(qy) =MC(qy) = 50 (firm X and Y’s marginal cost curves)
P=500-5Q, (market demand), where Q = qx + qy .
C(q) and have the same cost structure: marginal cost and average cost both=50
a.) Calculate the respective output levels of each firm if they collude to set monopoly prices.
b.) Calculate the respective output levels of each firm if they adhere to the Cournot model.
c.) What four possible output combinations are available in this game?
d.) Derive the for possible profit outcomes for each firm that arise from producing the four possible output combinations available in this game.
e.) Use these profit outcomes to construct a 2×2 normal representative matrix for this game.
f.) Does either firm have a dominant strategy? If so, what is it?
g.) Is there a Nash equilibrium for this game? If so, what is it?
h.) Is the outcome of this game a prisoner’s dilemma? Please Explain?
Please show all work to receive full credit.
