Refer to the normal-form game of price competition in the payoff matrix below. $\begin{array}{c}
\text { Firm B }\
\text { Firm A}
\begin{array}{|l|l|l|}
\hline & \text { Low Price } & \text { High Price } \
\hline & & \
\text { Low Price } & 0,0 & 50,-10 \
\hline & & \
\text { High Price } & -10,50 & 20,20\
\hline
\end{array}\end{array}$ What is the maximum interest rate that can sustain collusion?
A) 30 percent
B) 15 percent
C) 66.7 percent
D) 20 percent

Question

Refer to the normal-form game of price competition in the payoff matrix below. $\begin{array}{c}
\text { Firm B }\
\text { Firm A}
\begin{array}{|l|l|l|} 
\hline & \text { Low Price } & \text { High Price } \
\hline & & \
\text { Low Price } & 0,0 & 50,-10 \
\hline & & \
\text { High Price } & -10,50 & 20,20\
\hline
\end{array}\end{array}$ What is the maximum interest rate that can sustain collusion?
A) 30 percent
B) 15 percent
C) 66.7 percent
D) 20 percent

Quizplus · Accepted Answer

To sustain collusion, the present value of colluding must be greater than or equal to the one-time gain from deviating. Here, colluding means both firms choose High Price, earning each 20. If one deviates while the other keeps to High Price, the deviator earns 50. The gain from deviating is 50 - 20 = 30. Let r be the interest rate. The present value of colluding indefinitely is $20 + \frac{20}{1+r} + \frac{20}{(1+r)^2} + \ldots = \frac{20}{1 - \frac{1}{1+r}}$, simplifying to $\frac{20(1+r)}{r}$. Setting this equal to the one-time gain of 30 and solving for r gives $r = \frac{2}{3}$ or 66.7 percent.

Refer to the Normal-Form Game of Price Competition in the Payoff