= 2. Two firms operate in the coffee market. Let ai, for i 1, 2, be the investment in advertising. Profit functions depend on a and a2as follows: πι(α1,α2) = 4a1 + 3a102 (0₁)² π2(α1,α2) = 2a2 + a1a2(a₂)² a) Find reaction functions. b) Are a₁, a2 strategic complements or strategic substitutes? c) Find the equilibrium investment in advertising.
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- Considering that two competing companies sell a similar product in a market governed by the Cournot model in which the demand function is given by p = R$8,000 - 0.7 (q1+q2) and the cost of the product defined as R$1,700.00. The values resulting from this scenario are:The total cost for a product-testing firm is C(q)=70 + 20q2 q= number of products tested Price of a product = average cost Each corporation purchases one product test per year from a product-testing firm in the same city. All other inputs are ubiquitous. Suppose five corporations are initially distributed uniformly, with one corporation in each city (A,B,C,D,E). Is the initial distribution a Nash Equilibrium? Demonstrate it is not by finding how much one corporation would pay if they deviate and move to another city? What is the average price of having two tests conducted? (Which is the price that the corporation would pay if they "live" in a city where two tests are conducted) The average price of moving and thus, having two tests is: $_____What could lead the firms have asymmetric best response functions? What assumption(s) would have to change?
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- If you advertise and your rival advertises, you each will earn $5 million in profits. If neither of you advertises, you will each earn $10 million in profits. However, if one of you advertises and the other does not, the firm that advertises will earn $15 million and the non-advertising firm will earn $1 million. Which of the following is true? Multiple Choice A secure strategy for firm A is to not advertise. Firm A does not have a secure strategy. A secure strategy for firm B is to not advertise. None of the answers is correct.The Able Manufacturing Company and Better Bettors, Inc. are rival firms in the production of a calculator used by horse racing fans for handicapping (determining betting strategies). Each firm has a fixed cost of $100 and a MC = $10 in producing calculators. The demand for the industry’s product is: Q = 900 – 5P, where P is the market price and Q = Q1 + Q2. If each firm must choose how many calculators to produce and sell without knowing of its rival’s production decision, what will be the Cournot equilibrium price and quantities produced? Calculate the profit for each firm.Two manufacturers, denoted 1 and 2, are competing for 100 identical customers. Each manufacturer chooses both the price and quality of its product, where each variable can take any nonnegative real number. Let pi and xi denote, respectively, the price and quality of manufacturer i’s product. The cost to manufacturer i of producing for one customer is 10 + 5xi. Note in this expression that the cost is higher when the quality is higher. If manufacturer i sells to qi customers, then its total cost is qi(10 + 5xi). Each customer buys from the manufacturer who offers the greatest value, where the value of buying from manufacturer i is 1,000 + xi - pi; higher quality and lower price mean more value. A manufacturer’s payoff is its profit, which equals qi(pi - 10 - 5xi). If one manufacturer offers higher value, then all 100 customers buy from it. If both manufacturers offer the same value, then 50 customers buy from manufacturer 1 and the other 50 from manufacturer 2. Find all symmetric Nash…
- For the infinitely repeated game based on the stage game as shown, consider a symmetric strategy profile in which a player initially chooses x and continues to choose x as long as no player has ever chosen y; if y is ever chosen, then a player chooses z thereafter. Derive a condition on the discount factor for this strategy profile to be a SPNE.You are the manager of Taurus Technologies, and your sole competitor is Spyder Technologies. The two firms’ products are viewed as identical by most consumers. The relevant cost functions are C(Qi) = 2Qi, and the inverse market demand curve for this unique product is given by P = 110 −3 Q. Currently, you and your rival simultaneously (but independently) make production decisions, and the price you fetch for the product depends on the total amount produced by each firm. However, by making an unrecoverable fixed investment of $100, Taurus Technologies can bring its product to market before Spyder finalizes production plans. (Assume Taurus Technologies is the leader in this scenario.) What are your profits if you do not make the investment? $ What are your profits if you do make the investment? Instructions: Do not include the investment of $100 as part of your profit calculation. $Herfindahl index bounds. Suppose you only know the value of the market shares for the largest m firms in a given industry. While you do not possess sufficient information to compute the Herfindahl index, you can find a lower and an upper bound for its values. How?