Managerial Economics Question Set III

Managerial Economics Question Set III

A market has only 2 sellers. They are both trying to decide on a pricing strategy. If both firms charge a high price, then each firm will experience a 5% increase in profits. If both firms charge a low price, then each firm will experience a 3% increase in profits. If Firm 1 charges a high price and Firm 2 charges a low price, then Firm 1 will experience a 1% increase in profits and Firm 2 will experience a 6% increase in profits. If Firm 2 charges a high price and Firm 1 charges a low price, then Firm 2 will experience a 2% increase in profits and Firm 1 will experience a 7% increase in profits.

Construct a payoff matrix for this game.

Firm

High Price

Low Price

Firm

High Price

5% / 5%

1% / 6%

Low Price

7% / 2%

3% / 3%

Key:

Firm 1 / Firm

Increase in Profit

Decrease in Profit

Determine whether each firm has a dominant strategy and, if it does, identify the strategy.

This payoff matrix produces a dominant strategy for Firm 1, because when it charges lower prices, the result is either identical 3% gains for both firms when Firm 2 charges low prices, or a 7% to 2% disparity in favor of Firm 1. This is a dominant strategy for Firm 1 because no matter how Firm 2 responds to lower prices, it cannot produce higher gains than its competitor. Firm 2 has the same dominant strategy in this scenario, to charge lower prices, because this route produces identical 3% gains in profit when Firm 1 matches, and a 6% to 1% disparity in favor of Firm 2 when Firm 1 charges higher prices.

Determine the optimal strategy for each firm.

The optimal strategy for Firm 1 is to charge low prices while Firm 2 charges high prices, a scenario which generates a 7% increase in profits for Firm 1, as opposed to a 2% gain for its competitor. Conversely, the optimal strategy for Firm 2 is to charge low prices while Firm 1 charges high prices, a scenario which generates a 6% increase in profits for Firm 2, as opposed to a 1% gain for its competitor.

Determine the Nash equilibrium. (v) Is this a prisoner's dilemma? How do you know?

The Nash equilibrium in this payoff matrix is demonstrated when both Firm 1 and Firm 2 elect to charge high prices. In addition to producing identical 5% increases in profit for both firms, neither firm has an incentive to lower prices, and thus neither firm stands to gain by unilaterally adjusting its pricing policy.

2.) Respond to the charge that immigrants flood the labor market and drive down wages in the U.S.