The advertising agency raises its prices, causing a firm that chooses to run ads to earn $200 less in profits. Once the firms adjust to the higher advertising prices, what is the total combined profit of the two firms in the new Nash equilibrium?

Question

BlackTom AI · Accepted Answer

The question presents a 2x2 payoff matrix for Dave's Den and Rover's Rest and states that the advertising agency raises prices so that any firm that chooses to run ads earns $200 less in profits. We need to evaluate each option by examining how the price increase affects the strategic choices of the two firms.
Option 1: Run Ads, Run Ads cell originally shows (500, 400). With the price increase, the ad-running firm loses 200, so this cell becomes (300, 200). This makes both firms worse off if they both run ads, so we must compare to other options to see if this is a Nash outcome.
Option 2: Run Ads for Dave, No Ads for Rover cell originally (400, 500). After the price increase, Dave’s profit from running ads decreases by 200, yielding (200, 500). Rover doesn’t run ads here, so Rover’s profit remains 500. We must check best responses given the other’s choice.
Option 3: No Ads for Dave, Run Ads for Rover cell originally (700, 800). With the price increase, Rover’s profit from running ads drops by 200 to 600, giving (700, 600). Dave’s payoff remains 700 since he’s not running ads.
Option 4: No Ads, No Ads cell originally (900, 700). If neither runs ads, no one pays the higher ad price, so profits stay the same: (900, 700).
Now, identify best responses. If Rover runs ads, Dave’s payoffs are Run Ads → 300 and No Ads → 700. Dave prefers No Ads in this case. If Rover does not run ads, Dave’s payoffs are Run Ads → 200 and No Ads → 900. Dave still prefers No Ads. Therefore, Dave’s dominant strategy is No Ads.
Given Dave will choose No Ads, Rover’s payoffs are Run Ads → 600 and No Ads → 700. Rover prefers No Ads when Dave chooses No Ads. Thus, the Nash equilibrium is (No Ads, No Ads) with payoffs (900, 700).
The total combined profit in this Nash equilibrium is 900 + 700 = 1600. Therefore, the correct total is $1,600.
Examining the other options:
- $1,300 would correspond to scenarios where at least one firm’s action leads to lower totals than the equilibrium we found, which isn’t consistent with rational best responses given the price increase.
- $700 or $500 would imply outcomes with one or both firms earning far less than the equilibrium, which would not be sustainable as a Nash outcome since the other firm could deviate to improve its payoff.
- $1,500 is not supported by the computed equilibrium payoffs and would require an action profile that isn’t a mutual best response under the $200 ad-price penalty.
Thus, the computed Nash outcome is the combination that maximizes stability given the new payoffs, yielding a total of $1,600.

AP Economics-Hillebrand AP Microeconomics Sem 1 Exam 2025 - Requires Respondus LockDown Browser

The advertising agency raises its prices, causing a firm that chooses to run ads to earn $200 less in profits. Once the firms adjust to the higher advertising prices, what is the total combined profit of the two firms in the new Nash equilibrium?

查看解析

登录即可查看完整答案

类似问题

Consider a matrix form game between two players, A and B. Player A can choose between Up and Down, and Player B can choose between Left and Right. If the payoffs are represented using this matrix, what is the pure Nash equilibrium?

In the following duopoly game, the two firms can either set the price of their product high or low. For each firm, the final profit depends on the price they set as well as the price the other firm sets. The game is represented in the table below. The Nash equilibrium for this game is for:

Consider a sequential-move game with two players. The game tree with order of payoffs (Player 1, Player 2) is provided above. Choose the answer that is consistent with it.

Consider a simultaneous-move game with two players. The payoff table with order of payoffs (Player 1, Player 2) is provided above. Choose the statement that is consistent with it.

Consider the payoff matrix below. Which is correct for the following payoff matrix? Player 2 A B C Player 1 A (3,2) (3,1) (2,2) B (1,3) (2,2) (0,2) C (5,1) (8,1) (1,7)

Which pure strategy profiles are Nash equilibria? Select all that apply.

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单