The following depicts a normal-form game of price competition. $\begin{array}{l}
\quad\quad\quad\quad\quad\quad\text { Firm B}\
\text { Firm A}
\begin{array}{|l|l|l|}
\hline &\text { Low Price } & \text { High Price }\
\hline & & \
\text { Low Price } & 0,0 & 25,-5 \
\hline & & \
\text { High Price } & -5,25 & 10,10 \
\hline
\end{array}\end{array}$ What is the maximum interest rate that can sustain collusion?
A) 66.7 percent
B) 33 percent
C) 25 percent
D) 15 percent

Question

The following depicts a normal-form game of price competition. $\begin{array}{l}
\quad\quad\quad\quad\quad\quad\text { Firm B}\
\text { Firm A}
\begin{array}{|l|l|l|} 
\hline &\text { Low Price } & \text { High Price }\
\hline & & \
\text { Low Price } & 0,0 & 25,-5 \
\hline & & \
\text { High Price } & -5,25 & 10,10 \
\hline
\end{array}\end{array}$ What is the maximum interest rate that can sustain collusion?
A) 66.7 percent
B) 33 percent
C) 25 percent
D) 15 percent

Quizplus · Accepted Answer

To sustain collusion, the present value of future collusive profits must be greater than the one-time gain from deviating. Here, the one-time gain from deviating is 25 (moving from a collusive profit of 10 to a deviating profit of 25), and the loss from future punishment is 15 (moving from a collusive profit of 10 to a punishment profit of -5). The interest rate $ r $ that makes the present value of continuing with collusion equal to the one-time gain from deviation is found by solving $ \frac{25}{1+r} = 15 $. Solving for $ r $ gives $ r = \frac{25}{15} - 1 = \frac{10}{15} = \frac{2}{3} $, or 66.7 percent.

The Following Depicts a Normal-Form Game of Price Competition What Is the Maximum Interest Rate That Can Sustain Collusion