The following depicts a normal-form game of price competition. $\begin{array}{l}
\quad\quad\quad\quad\quad\quad\text { Firm B}\
\text { Firm A}
\begin{array}{|l|l|l|}
\hline &\text { Low Price } & \text { High Price }\
\hline & & \
\text { Low Price } & 0,0 & 25,-5 \
\hline & & \
\text { High Price } & -5,25 & 10,10 \
\hline
\end{array}\end{array}$ Suppose the game is infinitely repeated,and the interest rate is 5 percent.Both firms agree to charge a high price,provided no player has charged a low price in the past.If both firms stick to this agreement,then the present value of firm B's payoffs are:
A) 105.
B) 190.
C) 210.
D) 525.

Question

The following depicts a normal-form game of price competition. $\begin{array}{l}
\quad\quad\quad\quad\quad\quad\text { Firm B}\
\text { Firm A}
\begin{array}{|l|l|l|} 
\hline &\text { Low Price } & \text { High Price }\
\hline & & \
\text { Low Price } & 0,0 & 25,-5 \
\hline & & \
\text { High Price } & -5,25 & 10,10 \
\hline
\end{array}\end{array}$ Suppose the game is infinitely repeated,and the interest rate is 5 percent.Both firms agree to charge a high price,provided no player has charged a low price in the past.If both firms stick to this agreement,then the present value of firm B's payoffs are:
A) 105.
B) 190.
C) 210.
D) 525.

Quizplus · Accepted Answer

The present value of firm B's payoffs, when both firms stick to the agreement to charge a high price, is calculated using the formula for the present value of a perpetuity: $PV = \frac{C}{r}$, where $C$ is the cash flow per period, and $r$ is the interest rate. Here, $C = 10$ (the payoff for charging a high price) and $r = 0.05$ (the interest rate). Thus, $PV = \frac{10}{0.05} = 200$. However, the correct calculation should account for the fact that the payoff is received at the end of each period, making the formula $PV = \frac{C}{r}$ directly applicable, leading to the correct calculation as $PV = \frac{10}{0.05} = 200$, indicating a mistake in the provided choices.

The Following Depicts a Normal-Form Game of Price Competition Suppose the Game Is Infinitely Repeated,and the Interest Rate Is