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- QUESTION 8 S1, S2, S3 and S4 are UIUC students who just graduated. They each have a poster of Dolly Parton that they are willing to sell. B1, 82, B3 and B4 are new students at UIUC and want to buy Dolly Parton postern for their rooms. The tables below give the minimum selling prices and maximum buying prices for each student. Minimum Selling Prices Maximum Buying Pricen X+$9 S1 $10 B1 S2 $11 B2 X+$14 S3 $20 B3 X+$16 S4 $25 B4 X+$26 If X is negative $5 (.e., Xu-$5), what is the market-clearing price? Note: Do not include the dollar sign,You are considering two options for your next family vacation. You can visit Disney World or Chicago. Your utility from Disney World is 100 if the weather is clear, and 0 if it rains. Chicago is worth a utility of 70 if the weather is clear and a utility of 40 if the weather is rainy. Also assume that the chance of rain at Disney World is going to be 50% and the chance of rain in Chicago is 40%. As a utility maximizer, should you plan to go to Disney World or Chicago? (Explain using relevant equations)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.…
- Suppose that you own a used car dealership. You want to sell a 2005 Honda Civic LX. You know that this car is of high quality, and it cost you $5000 to acquire it (so you will not sell it at a price below $5000). However, consumers cannot see the quality of the car at the time of purchase. They believe that 25% of the cars in the used car market are high-quality cars and 75% are low-quality cars or “lemons.” A typical lemon costs $2000 to acquire (so you will not sell it at a price below $2000). Consumers are eager to buy and are willing to pay up to $3000 for a lemon and $6000 for a high-quality car. From now on, suppose that only you (the seller) know the quality of the cars. (Buyers do not know the quality, but know the proportion of high- and low-quality cars in the market). Suppose that you could offer bumper-to-bumper warranties. You know that offering a warranty on a high-quality car costs, on average, $450 per year of warranty offered, while a warranty on a lemon is very…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…
- You and your roomate are deciding whether to go to a party or not on Friday. Going to the party is fun and gives a benefit of 4. If you go to the party, there is a 50% chance you will get covid. If you do not attend the party but your roommate does and gets covid, there is 80% chance that you will get covid. The impact of getting covid is -10. If both of you stay home, you will not be exposed to covid and will not have fun, leading to a payoff of 0 for both of you. 3. Construct a game matrix based on the description above and find any (c) Nash equilibria. How would your answer change if one roomate was less social and enjoyed (d) partying less than the other? Change the payoff matrix in a way that is both consistent with one roommate being less social than the other and changes the prediction you found in (a). (Note: if you found multiple possible equilibria in (a), changing the outcome could mean either making one of your prior Nash equilbria the only Nash equilibrium or making an…Jack and Diane work at a bakery. Jack can make either five batches of cookies or two cakes per hour, while Diane can make either four batches of cookies or three cakes per hour. At 9:00 a.m. they receive an order for 24 batches of cookies and nine cakes. What time is the soonest they can have the order ready?An investor allocates $30,000 and $50,000 to two assets (A1 and A2). These assets generate 5% and -4.5% rate of returns, respectively. She allocates the remaining 50% of her portfolio to an asset (A3), which provides 4.5% rate of return. Calculate the portfolio's rate of return.
- The research department at a manufacturing company has developed a new process that it believes will result in an improved product Management must decide whether to go ahead and market the new product. The new product may or may not be better than the old one. If the new product is better and the company decides to market it, sales should increase by $50,000. If it is not better and they replace the old product with the new product on the market, they will lose $24,000 to competitors. If they decide not to market the new product, they will lose a total of $30,000 if it is better and just research costs of $10,000 if it is not. Answer parts a through c below. (a) Prepare a payoff matrix. (Type an integer or decimal for each matrix element. Do not include the $ symbol in your answer.) (b) If management believes there is a probability of 0.4 that the new product is better, find the expected profits under each strategy and determine the best action. Select the correct answer below and fill…Matthew is playing snooker (more difficult variant of pool) with his friend. He is not sure which strategy to choose for his next shot. He can try and pot a relatively difficult red ball (strategy R1), which he will pot with probability 0.4. If he pots it, he will have to play the black ball, which he will pot with probability 0.3. His second option (strategy R2) is to try and pot a relatively easy red, which he will pot with probability 0.7. If he pots it, he will have to play the blue ball, which he will pot with probability 0.6. His third option, (strategy R3) is to play safe, meaning not trying to pot any ball and give a difficult shot for his opponent to then make a foul, which will give Matthew 4 points with probability 0.5. If potted, the red balls are worth 1 point each, while the blue ball is worth 5 points, and the black ball 7 points. If he does not pot any ball, he gets 0 point. By using the EMV rule, which strategy should Matthew choose? And what is his expected…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.
