QUESTION 3 Let c(w1; w2; y) be a cost function, and let A > 1. We have: Oa.q A w; Aw2; y) = o(w1; w2; y) O b.q A w1; Aw2; y) = Ac(w1; w2; y) Oc. d A w1; Aw2: y) > Ao(w1; w2; y) Od.( A w1; Aw2: y) < Ao(w1; w2; y)
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- Question I am in possession of two coins. One is fair so that it lands heads (H) and tails (T) with equal probability while the other coin is weighted so that it always lands H. Both coins are magical: if either is flipped and lands H then a $1 bill appears in your wallet, but when it lands T nothing happens. You may only flip a coin once per period. The interest rate is i per period. You are risk-neutral and thus only concern yourself with expected values (and not variance). For simplicity, in the questions below assume you will live forever. 1. How much are you willing to pay for such a coin that you know is fair? 2. How much are you willing to pay for such a coin that you know is weighted? 3. I currently own the coins and know which is fair and which is weighted, but you cannot tell which is which. You may make an offer to purchase a coin of your choosing, which I am free to accept or reject. What is the most you are willing to offer? Explain how you arrived at this answer. 4.…Let's say we have a game called "guess 2/3 of the average," where players can choose any number x ∈ [0, 100]. 5% of players are at level N0, 40% at level N1, 35% at level N2, 15% at level N3, and 5% at level N4. Players at level N0 choose a number randomly, while players at higher levels choose a number according to their beliefs, which are as follows: players at higher levels believe that all other players are one level lower than themselves. (a) What will be the winning number and which level players will be the winners? (b) Under the assumptions of classical game theory, the mentioned version of the game "guess 2/3 of the average" has exactly one equilibrium, in which everyone chooses the number 0. Prove that this outcome is indeed a Nash equilibrium of the game.Once your producers understand the “I WANT $3” game, you will present the “I WANT TO BE A MILLIONAIRE” game. Its rules are: There are two contestants/opponents (who do not know each other and cannot communicate with each other during the game). Each player is given $1 million at the start of the game. Independently and simultaneously, each player must choose to add to their award $0, $1, $2, $3, $4, ……$999,999, or $1,000,000. Doing so decreases the other player’s award by twice that amount. Each player ends the game with a payoff based on their initial one million, the additional amount that they announced, and the reduction due to the opponent’s announcement. The game matrix for this expanded game has 1,000,001 rows, 1,000,001 columns, and 1,000,002,000,001 pairs of payoffs. I STRONGLY RECOMMEND THAT YOU DO NOT DRAW IT! But building on what you learned in part (a), answer the following two questions: i) What is the Nash equilibrium of this game? ii) What are the Nash…
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- Two travelers own an identical suitcase that contains identical antiques. The airline is liable for a maximum of $100 per suitcase. To determine how much to reimburse each traveler, the airline puts them in different rooms (so that they cannot communicate), and ask them to write down an amount (an integer number) between $2 and $100. If both write down the same number, the airline will reimburse both travelers that amount. However, if the two amounts are different, both travelers will be paid the lowest of the two numbers along with a bonus/malus: $2 extra will be paid to the traveler who wrote down the lower value and a $2 deduction will be taken from the person who wrote down the higher amount. What are the travelers’ best response functions? What are the Nash equilbria of the game? Are they Pareto efficient? Explain the intuition why.**Practice** In order to alleviate their risks, they are considering a risk-sharing agreement. Carol would buy one CC and David would buy one DD. Six months from now, they would sell their coins, add up the total amount of money, and split it equally between them. Thus, if only one of the coins is successful, they would both still have some positive amount of money at the end. Assume that they can verify whether the other really made the investment. They know whether the investment is successful, since the price of the coin is public information, and they trust that the other will pay them as promised. Which of the following statements is accurate?A. They will not make that risk-sharing agreement.B. Carol is willing to take the risk-sharing agreement, but David is not.C. They may be willing to make that risk-sharing agreement, but it depends on information not given in the question.D. They will surely make the risk-sharing agreement.E. None of the statements above is correct.A computer reseller needs to decide how many laptops to order next month. The lowest end laptop costs $220 and the retailer can sell these for $300. However, the laptop manufacturer already announced that they are coming out with a new model in a couple of months. Any laptops that will not be sold by the end of next month will have to be heavily discounted at half-price. The reseller also needs to consider that every time he fails to fulfill a laptop order, he stands to lose $25 for every unit. Based on the past months’ sales, the reseller estimates the demand probabilities for sales (S) as follows: P(0 units) = 0.3; P(1 units) = 0.4; P(2 units) = 0.2; P(3 units) =0.1. The reseller thinks it’s a good idea to conduct a survey on whether or not his customers are going to buy laptops and how many. The survey results will either be Yes (Y), No (N) or Don’t Know (DK). The probability estimates of the results based on the demand for number of units are: P(Y|S = 0 units) = 0.1 P(Y|S = 1…
- In the late 1990s, car leasing was very popular In the United States. A customer would lease a car from the manufacturer for a set term, usually two years, and then have the option of keeping the car. If the customer decided to keep the car, the customer would pay a price to the manufacturer, the "residual value," computed as 60% Df the new car price. The manufacturer would then sell the retumed cars at auction. In 1999, manufacturers lost an average of $480 on each returned car (the auction price was, on average, $480 less than the residual value). Suppose two customers have leased cars from a manufacturer. Their lease agreements are up, and they are considering whether keep (and purchase at 60% of the new car price) their cars or return thelr cars. Two years ago, Becky leased a car valued new at $18,500. If she returns the car, the manufacturer could likely get $12,950 at auction for the car. Eleen also leased a car, valued new at $19,000, two years ago. If she returns the car, the…Nn3 Suppose an incumbent monopoly firm currently earns a profit of $50,000 per period. A potential entrant could enter and make a profit of $15,000 per period while also lowering the incumbent’s profit to $20,000 per period. The monopoly firm could seek to engage in predatory pricing, which would lead to both firms earning a loss of $5,000 per period. (a) Is there a Nash Equilibrium in this game? If so, what is it? (b) Discuss how this game might play out in the real world?the video link is: https://www.youtube.com/watch?v=aqEz6kvXhc8please give me detailed solutions and calculations, thank you!
