2) Now suppose the prices change to q= (91, 92) = (2,1). Again, obtain the optimal choices for A and B, denote them by c = (C₁, C2) and d= (d₁, d2). Solve for c and d.
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- Problem 2: Brian wants to use his recent knowledge of utility to develop his own utility function for how many hours he should study for future tests. He mainly cares about two attributes: the number of hours he studies (x), and the mark (out of 100) that he gets (y). His research of utility functions shows that when a decision maker has to decide based on more than one attribute, a multi-linear multi-attribute utility function can be developed. This function follows the form U(x, y) = kxUx(x) + kyUy(y) + (1 − kx-ky)Ux(x)Uy(y), where Ux(x) and Uy(y), are independent utility functions for attribute x and attribute y, and kx and ky are constants. If Brian just considers the number of hours he studies, he believes his utility function for the number of hours he studies is: Ux(x) : = 1 x² - where 0 ≤ x ≤ 4. If Brian just considers the 16 = mark he gets, his utility function is: Uy(y) : ) y , where 0 ≤ y ≤ 100. Brian is indifferent J 100 between (i) studying 0 hours and getting a mark of 49…Sean is arguing with his girlfriend, Yvette. They have been going out for a little more than two years. YVETTE: I'm leaving you, Sean. Get over it. SEAN: Are you saying that being single will make you happier than you've been with me? Speaking personally, I think the utility we've had in this relationship was much more than you could have had if you'd been single this whole time! YVETTE: I had taken an economics class and the word "utility" rings a bell. It's not that at all. We've had a fine time. It's that the utility I would get by continuing our relationship isn't worth it anymore. SEAN: I've never been dumped by someone citing the law of before. You're a piece of work, you know that? Yvette doesn't hear. She has already walked off, leaving Sean feeling like something of a sunk cost.A consumer has a choice of spending $20,000 on a Honda or $14,000 on a Kia. She was observed buying a Kia during the weekend. Does this mean the consumer prefers the Kia to the Honda?
- You must allocate the 70,000 seats in Reliant Stadium (in Houston) among Texan (Houston) and Cowboy (Dallas) fans for an upcoming game between the two footfall teams. You can set different prices for seats in the Dallas and Houston sections of the stadium. Suppose you can obtain $40/ticket from Houston fans irrespective of the number of seats you allocate to Houston fans. You must drop price in order to sell more tickets to Dallas fans, however. Let Q be the number of tickets you allocate to Dallas fans. Assume that the maximum price you can charge for these tickets is given by the following inverse demand function P= 80 500 (a) Express the total revenue (on all 70,000 seats) from ticket sales as a function of Q; (b) Derive the first-order condition of the revenue-maximizing problem (it's a function about Q); (c) What is the optimal number of seats allocated to Dallas fans?Question 10 Which of the following startements about network externalities is CORRECT? Air pollution is an example of a network externality. For a good with network externalities, the number of people who are willing to buy a unit of the good is uniquely determined by the price. Network externalities are always positive. The manufacturer of a new good with network externalities might give away a free version of the good. For a good with network externalities, one person's valuation of the good is always increasing in the number of other people using the good.Question-1 It is given that a typical consumer has a well-behaved preference structure for his consumption bundle which includes only two goods, A and B. Further assume that commodity A is normal and commodity B is inferior. By keeping commodity A on the x-axis and commodity B on the y-axis you are required to show the price decomposition for commodity B when $PB increases exogenously relative to $PA. Provide a well-labelled and fully explained-legible diagram.
- There are two shows on Netflix that Jeff can watch, Show 1 and Show 2. x₁ measures the number of episodes watched of Show 1 and x₂ measures the number of episodes watched of Show 2. Jeff's preferences can be represented by u(x₁, x₂) = x² + ax². Jeff has 5 hours available for watching Netflix today. Each episode of Show 1 lasts 30 minutes, while each episode of Show 2 lasts one hour. For all question parts, round to three decimal places if necessary. For parts (a) - (f), let a = 1. Draw Jeff's indifference curves for the utility levels u = 4, 9, 16. Draw a straight line between the bundles (x₁, x₂) = (4,0) and (x₁, x₂) = (0,4). Now, use your picture to determine whether the following two statements are true or false. Answer "1" for true. Answer "0" for false. a) Statement 1: Jeff's preferences are strongly monotone. b) Statement 2: Jeff's preferences are strictly convex. c) Find the bundle at which one of Jeff's indifference curves is tangent to the budget line. (x₁, x₂)=( d) Evaluate…There are two shows on Netflix that Jeff can watch, Show 1 and Show 2. x₁ measures the number of episodes watched of Show 1 and x2 measures the number of episodes watched of Show 2. Jeff's preferences can be represented by u(x₁, x₂) = x² + ax². Jeff has 5 hours available for watching Netflix today. Each episode of Show 1 lasts 30 minutes, while each episode of Show 2 lasts one hour. For all question parts, round to three decimal places if necessary.The following five individuals have different utility functions over food (good x) and clothing (good y): 1) u₁(x, y) = 3x²y 2) u₂(x, y) = 2√x + y 3) Uz(x, y) = x0.6y0.4 4) u₁(x, y) = x² + y² 1 5) us(x, y) = x + 3y For each of these people: a) Compute their marginal utilities of good x, MUx = Ju(x,y) MU, = ду du(x,y) ax b) Check whether the property of "more is better" is satisfied for both goods? Explain. [Hint: Check whether marginal utilities are positive assuming positive amounts of good x and good y] ƏMUX əx and marginal utility of good y, c) Does the marginal utility of good x diminish, remain constant, or increase as each of the individuals buys more x? Explain. [Hint: There are 2 ways to do it: 1) visually check what happens to the expression of MUx when x increases (does it decrease, keep constant or decrease?); or 2) take the partial derivative of this marginal utility with respect to x, that is ƏMUx .aMUX ƏMUX If 0, the marginal utility of x is increasing in x] d) Does the…
- Rick thinks either Morty or Summer broke his TV. Morty and Summer each have to decide simultaneously whether to take the blame or blame the other person. If they both blame the same person (both blame Morty or both blame Summer), the person they blame gets a small punishment and utility of -2, while the blameless person gets a utility of 0. Otherwise (if they both blame the other or both blame themselves), they both get a more severe punishment and a utility of -10.Rick thinks either Morty or Summer broke his TV. Morty and Summer each have to decide simultaneously whether to take the blame or blame the other person. If they both blame the same person (both blame Morty or both blame Summer), the person they blame gets a small punishment and utility of -2, while the blameless person gets a utility of 0. Otherwise (if they both blame the other or both blame themselves), they both get a more severe punishment and a utility of -10.a. Draw the normal (matrix) form of this game, with Morty choosing the row and Summer choosing the column. Does either Morty or Summer have a dominant strategy? Explain your answer. Note: only Morty and Summerare players in this Game. Rick designed the game and is not a player. b. Find all Nash equilibria of this game. c. Suppose instead there are three suspects: Morty, Summer, and Jerry. Otherwise, the rules are the same as before. Draw the normal (matrix) form of the game. Hint: draw three matrices, with Morty choosing the…Rick thinks either Morty or Summer broke his TV. Morty and Summer each have to decide simultaneously whether to take the blame or blame the other person. If they both blame the same person (both blame Morty or both blame Summer), the person they blame gets a small punishment and utility of -2, while the blameless person gets a utility of 0. Otherwise (if they both blame the other or both blame themselves), they both get a more severe punishment and a utility of -10. a.Draw the normal (matrix) form of this game, with Morty choosing the row and Summer choosing the column. Does either Morty or Summer have a dominant strategy? Explain your answer. Note: only Morty and Summer are players in this Game. Rick designed the game and is not a player. b.Find all Nash equilibria of this game. c.Suppose instead there are three suspects: Morty, Summer, and Jerry. Otherwise, the rules are the same as before. Draw the normal (matrix) form of the game. d.Find all Nash equilibria of the three-player…