The above figure shows the reaction functions for two pizza shops in a small isola town. The Stackelberg leader will produce A) 100 pizzas. B) 50 pizzas. OC) 25 pizzas. D) 66.7 pizzas.
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- 2. Subgame Perfect Equilibrium (a) Find Subgame Perfect Equilibrium P1 (2,4) L P2 Out X (0, Q1 (10-Q₁1)) C P2 Y Ꭱ (4,4) (3,1) (2, 2) (-1,-1) (b) Entry with fixed cost Find Subgame Perfect Equilibrium P1 In Q2 U P1 P2 P₂ D (23 (10Q2 Q3) — 3, Q2 (10- Q2 - Q3))Harry and Rebecca are working on a joint project. Harry is responsible for the hardware, his choices are between an Apple (A), IBM (B) or Cisco (C). Rebecca will be developing the software choosing between existing software development tools YouCreate (Y) or Zoho Creator (Z). Harry expects her to choose an appropriate software without consulting him. However, YouCreate is incompatible with IBM hardware, but works well with Apple products. Rebecca prefers YouCreate For Apple hardware, otherwise she prefers Zoho Creator. The problem is that Harry has been looking for hardware on his own and has not informed Rebecca which hardware he bought. If Harry bought a Cisco product, it comes with its own software development product. Payoffs are as follows: if Harry bought a Cisco product, they each receive $3, irrespective of the software development tool Rebecca has brought. If Harry bought an apple hardware and Rebecca a YouCreate tool then Rebecca receives $2, and Harry $4. If Rebecca has…(a) Assuming that each fishery chooses fi ∈ (0, F), to maximize its payoff function, derive the players’ best response functions and find a Nash equilibrium. (b) Is the equilibrium you found in (a) unique or not? What are equilibrium payoffs? 4 (c) Suppose that a benevolent social planner wants maximize the utility of both fisheries. In other words, the social planner solves the following problem: max w(f1,f2) w(f1, f2) = u1(f1, f2) + u2(f1, f2) =2 ln(f1) + 2 ln(f2) + 2 ln(F − f1 − f2). Find the social planner’s solution. (d) What are the fisheries’ payoffs if the quantities of fish they catch are solutions to the social planner’s problem? What can you say about the Nash equilibrium quantities of fish being caught as compared to the social planner’s solution? (e) If fishery j decides to follow the recommendation of the social planner, how much fish will firm i catch?
- For a certain company, the cost for producing x items is 60x + 300 and the revenue for selling x items is 100x – 0.5x². - The profit that the company makes is how much it takes in (revenue) minus how much it spends (cost). In economic models, one typically assumes that a company wants to maximize its profit, or at least wants to make a profit! Part a: Set up an expression for the profit from producing and selling x items. We assume that the company sells all of the items that it produces. (Hint: it is a quadratio polynomial.) Part b: Find two values of x that will create a profit of $300. The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2; 4; 6 or x + 1; x – 1). The order of the list does not matter. To enter va, type sqrt(a). x = Part c: Is it possible for the company to make a profit of $15,000?Amazon could launch a smartphone this year that costs “a fraction” of what Apple charges for its iPhone, a new report says. Amir Efrati at The Information spills details from an allegedly leaked internal Amazon document. The paperwork is said to have been produced by a potential partner and two people who were involved in discussions with Amazon. According to Efrati, the document discussed strategies for penetrating smartphone markets in China, Europe and the United States. Earlier discussions also mentioned Latin America as a possibility. The phone, which has been referred to as “Project Aria,” is likely to go on sale this year, according to Efrati. There’s no specific price, but he says Amazon is “determined” to “keep the phone at a small fraction of the iPhone’s $550-and-up price tag.” If Amazon does launch a smartphone this year, it’s unclear if it will fall under the company’s own brand or if it will work with a partner. Efrati says Amazon was “in talks” with “multiple hardware…Two rival companies competing in the same market need to decide their plans for future expansion of their stores. The Table below shows the possible outcomes of their mutually interdependent actions (payoffs are profits in £m) Giga Company Titanic Conglomerate No Change Refurbishment of existing stores Large Expansion No Change 30, 40 25, 35 15, 24 Refurbishment of existing stores 35, 30 28, 32 18, 33 Large Expansion 12, 22 18, 20 20, 25 The Nash equilibrium: (A) does not exist. (B) occurs when both firms choose Refurbishment of existing stores. (C) occurs when both firms choose Large Expansion. (D) occurs when both firms choose No Change.
- Exercise 3.1 List all the reduced pure strategies, then reduce the tree to strategic form. START b ㅍ 9 e d e I (2, 0) (3, 0) h h J k k (1, 1) (0, 2) 1 (0, 2) (1, 1) (2,0) (1, 1) (1, 1) (2,0)Table 3. This table shows a game played between two firms, Firm A and Firm B. In this game each firm must decide how much output (Q) to produce: 5 units or 6 units. The profit for each firm is given in the table as (Profit for Firm A. Profit for Firm B). Firm A Q=5 Q=6 Firm B Q=5 (24, 24) (30, 10) Q=6 (10,30) (19, 19) Refer to Table 3. The dominant strategy For Firm A is to produce Select one: O a. 5 units and the dominant strategy for Firm B is to produce 5 units. b. 5 units and the dominant strategy for Firm B is to produce 6 units. c. 6 units and the dominant strategy for Firm B is to produce 5 units. d. 6 units and the dominant strategy for Firm B is to produce 6 units.A pizza shop sells two types of pizzas: Chicago-style and New York-style. The owner makes $8.00 Profit on each Chicago- style pizza pie & $5.50 Profit on each New York-style pizza pie. The owner would love to sell an unlimited amount of pizza but unfortunately they are limited by two production constraints: Prep Time and Cook Time. Each Chicago-style pizza requires 4 minutes of Prep Time, each New York-style pizza requires 3 minutes of Prep time, and there is only 600 minutes of Prep Time available. Each Chicago-style pizza requires 5 minutes of Cook Time, each New York-style pizza requires 2.5 minutes of Cook Time, and there is only 550 minutes of Cook Time available. Based on the profit contributions & constraints given in the information above, what is the pizza shop's expected profit if it produces at the optimal amount? $800 $1120 $1560 $1100 O $1320
- enata and Jerome operate a company that makes miniature electronic surveillance drones from a warehouse in an industrial estate. Each drone costs them $49 to make and has additional fixed costs of $275 (per drone). On average, Renata and Jerome sell 85 drones per week for a price of $64 each. Renata and Jerome then decide to have a sale and reduces the price of each drone to an even numbered price between $54 and $60 inclusive. During the sale, they sell on average 150 devices per week. Q.Plot Total Cost, Total Revenue and Profit Functions on the same set of axes and Find the Marginal Revenue (MR) and Marginal Cost (MC) functions by differentiation and determine the level of output q at which MR = MC. With reference to your Excel plot, what conclusion can you make about this value?Thelma and Louise are competitors in a local beer market and each is trying to decide if it is worthwhile to advertise. If both of them advertise, each will earn a profit of $2000. If neither of them advertises, each will earn a profit of $5000. If one advertises and the other doesn't, then the one who advertises will earn a profit of $7500 and the other will earn a profit of $1000. To make the most money, what should Thelma do and how much profit will she earn? Select one: a. she should advertise, and she will earn $7500 b. she should do whatever Louise does, and will earn either $2000 or $5000 C. she should not advertise, and she will earn $5000 d. she should advertise, and she will earn $2000 Next pageConsider the game R T 11 1.0 10 M 014.0 0.1 B 0.10. 4.0 (a) Find the Nash equilibrium in pure strategies. (b) Find the Nash equilibrium in completely mixed strategies. (c) Find the Nash equilibrium in partially mixed strategies ove the support {A. B} x {C.R).