2. Suppose that two products, i= 1, 2, are located at the extreme ends of the [0,1] interval. Let li denote the location of the product and x the consumer locations. Consumers buy one unit and are uniformly distributed on the unit interval; their indirect utility is given by r - pit |li - xl, where r is the willingness to pay, pi the price set by firm i, and t a parameter that measures the disutility from not consuming their ideal product. Marginal cost of production is constant and equal to c. Solve for the Stackelberg equilibrium in prices where the firm located at zero is the leader firm. Is there an advantage for being a price leader, that is, is there a first-mover advantage? Why? Explain. Compare the results with simultaneous choice of prices.
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- 1 Assume there are two firms in a Hoteling Linear city. One firm is located at zero and the other at one. Assume the following utility equations: U0=v−p−tx+μ, U1=v−pn−t(1−x). Where U0 is utility from buying the good from the firm located at zero, p is the price for the firm at point zero, t is the travel cost and μ is bonus utility because the firm at point zero makes people a little bit happier. U1 is utility from buying the good from the firm at point one and pn is the price. Part a) Find the indifferent consumer1) The quantities demanded, q1 and q2, of two products depend on their unit prices, p1 and p2, as follows q1 = 135 − 2p1 − p2, q2 = 205 − p1 − 3p2. The total revenue is defined as R = q1p1 + q2p2. A. How should the prices be set to generate the maximum possible revenue? Apply the Second Derivative Test to show that your answer yields the maximum and not the minimum revenue. B. What is the maximum possible revenue and what are the corresponding values of q1 and q2? 2) Find the maximum and minimum values of the function f(x, y, z) = ax + by + cz, where a, b, c are three positive numbers, on the unit sphere x^2 + y^2 + z^2 = 1.2.Suppose the firm uses a two-part tariff to implement first-degree price discrimination. Determine the tariff to be applied to each type of consumer. Determine the profit that the firm will achieve. 3. How could the firm achieve the same result using take-it-or-leave-it offers?4. Now suppose the firm cannot identify each consumer’s utility function. What take-it-or-leave-it offers should the firm propose to ensure incentive compatibility? How much profit does the firm make?
- 1.Suppose that Chris's utility function is given by UC=QC1/2 RC1/2 , where QC and RC are his consumption of Q and R, respectively. Dana's utility function is given by UD=QD1/3 RD2/3, where QD and RD are her consumption of Q and R, respectively. Write an equation for the marginal rate of substitution (MRS) between Q and R for each of the two agents. 2.Suppose that the price of good R is pR=1 and the price of good Q is pQ=2. How much is Chris's and Dana's initial income, given his endowments and given these prices? 3. At these prices, how many units of Q would Chris and Dana want to consume? 4. At these prices, how many units of R would Chris and Dana want to consume?Revealed Preference Methods What types of values can revealed preference (RP) methods measure? What is the basic idea behind RP methods? What is the basic intuition for how the hedonic pricing method works? Give examples of the types of products that are amenable to a hedonic pricing analysis. What are some of the limitations of the hedonic property pricing method? What is the basic intuition for how the travel cost method (a recreation demand method) works? Stated Preference Methods Compare and contrast revealed and stated preference. Broadly speaking, what are the relative advantages and disadvantages of each? What are the five stages of a contingent valuation analysis? Why are in-person interviews considered to be a superior method of collecting data for a contingent valuation study relative to telephone, mail, or internet surveys? Among the various methods of eliciting WTP/WTA in a CV study, which is considered to be the “gold standard,” and why? What do scope, convergent validity,…Joanna is playing blackjack for real money. She has reference-dependent preferences overmoney: if her earnings are m and her reference point is r, then her utility is v(m − r), wherethe value function v satisfies v(x) = √x for x ≥ 0, and v(x) = −2√−x for x ≤ 0a) Graph Joanna’s utility function as a function of m − rb) Does Joanna’s utility function satisfy loss aversion? Does it satisfy diminishingsensitivity?Suppose that Joanna has linear probability weights (that is, she does NOT have prospecttheory’s non-linear probability weighting function). Hence, if she has a fifty-fifty chance ofgetting amounts m and m′, and her reference point is r, her expected utility is1/2v(m − r) + 1/2v(m′− r) (2)For parts (c), (d), and (e), assume that Joanna’s reference point is $0 (that is, no winsor losses) and answer the following questions for each part: (i) What is the g for whichJoanna would be indifferent between not gambling and taking fifty-fifty win $g or lose$4 gamble? (ii) Does this reflect…
- Let's say that the demand side of the market for Blue Soda is comprised of 3 leading agents/individuals: Anthony, Brad, and Claire. Let P be the price of 1 liter of Blue Soda, and Qd be the quantity demanded of Blue Soda in liters. Here are the key points to the problem: - Anthony buys only one liter of Blue Soda if the price of it falls below his choke price of $10. - Brad's demand for Blue Soda is defined by QdB = 5 - P/2 - Claire buys 2 liters if the price is below $5, 1 liter if the price is between $5 and $10, and nothing if the price is above $10. Using this information, please sketch the individual demands and the market demand by aggregating the three agents/individuals. Label the graph clearly. Please make sure to sketch the individual demands first and then sketch the market demand.Every month, a family of three spends $2,000 on food (F) and other items (O). The family’s preferences are represented by the utility function U(F,O) = F1/5O4/5. The unit price of food and the unit price of other items are both $1. Find this family’s monthly food expenditure.The family could join a consumers’ club. At the club, food costs 20% less than in other stores (i.e., at the food club PF = $0.8)Brit-Brick is a company that produces bricks and cement in the UK. Their largest consumer is ConstrUK, a UK construction company. The manager of Brit-Brick has asked the research department to find out how sensitive ConstrUK’s demand for bricks is. The research department has estimated that ConstrUK’s preferences over bricks (x) and cement (y) can be described by the utility function U(x,y)=x^(7/10)y^(1-7/10) The price for one bag of cement is equal to £1. It is estimated that ConstrUK’s budget is £10,000. Find the price-consumption curve for bricks and the corresponding demand curve.
- Let the utility function be given byu(x1, x2) = √x1 +√x2.Let m be the income of the consumer, p1 and p2 the prices of good 1 and good 2, respectively.(a) Write down the budget constraint and illustrate the set of feasible bundles usinga figure.(b) Suppose that m = 24, p1 = 2 and p2 = 4 . Find the optimal bundle for theconsumer. In other words, find the combination of x1 and x2 that maximizes the consumer’sutility when the prices are p1 = 2 and p2 = 4, and her income is m = 24.(c) Determine the Marshallian demand function.(d) Determine the expenditure function.Every month, a family of three spends $2,000 on food (F) and other items (O). The family’s preferences are represented by the utility function U(F,O) = F1/5O4/5. The unit price of food and the unit price of other items are both Suppose the club did NOT charge a membership fee: how much money would the family spend on food? How much food would the family buy? (The following data pertain to products A and B, both of which are purchased by Madame X. Initially, the prices of the products and quantities consumed are: PA = $10, QA = 3, PB = $10, QB = 7. Madame X has $100 to spend per time period. After a reduction in price of B, the prices and quantities consumed are: PA = $10, QA = 2.5, PB = $5, QB = 15. Assume that Madame X maximizes utility under both price conditions above. Also, note that if after the price reduction enough income were taken away from Madame X to put her back on the original indifference curve, she would consume this combination of A and B: QA = 1.5, QB = 9 Determine the change in consumption rate of good B due to (1) the substitution effect and (2) the income effect. Determine if product B is a normal, inferior, or Giffen good. Explain.