Suppose that consumer utility is given by U₁ = v₁ - p + an common sensitivity to network effects Suppose that platform has zero costs where u, U[0, 1]- a uniformly distributed consumer valuation, a and 0 ≤ n ≤ 1 is the number of consumers joining the platform. of serving consumers. Assume that consumers' outside option is 0. Now consumers simultaneously decide whether to join the platform... 1. Show that both full participation and zero participation equilibria can co-exist only if a > p > 1. 2. Show that interior, i.e. partial participation, equilibrium can only exist if a < 1. What is the price in this equilibrium?

Suppose that consumer utility is given by U₁ = v₁ - p + an common sensitivity to network effects Suppose that platform has zero costs where u, U[0, 1]- a uniformly distributed consumer valuation, a and 0 ≤ n ≤ 1 is the number of consumers joining the platform. of serving consumers. Assume that consumers' outside option is 0. Now consumers simultaneously decide whether to join the platform... 1. Show that both full participation and zero participation equilibria can co-exist only if a > p > 1. 2. Show that interior, i.e. partial participation, equilibrium can only exist if a < 1. What is the price in this equilibrium?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Answer the given question with a proper explanation and step-by-step solution. Angela and Betty are deciding how many nights to stay at a resort. Given above are the budget lines and indifference curves for both Angela and Betty. They are not travelling together and therefore will make independent decisions (they do not have to stay the same number ofnights) L1 is the budget line for each of them before any discounts are offered. Each of them is offered a “Buy Three Nights Get One Free” deal, where if they stay for three nights the fourth night is free. This is just a one-time discount and all subsequent nights after the fourth night are at the undiscounted price. The budget line after the discount is the heavily shaded blue line L2. You may assume that each consumer wishes to maximize their utility (satisfaction) when determining the number of nights they will stay. (a) With the budget line at L1 how many nights will Angela stay?(b) With L1 the budget line how many nights will Betty…
- Individuals 1 and 2 are forming a company. The value of their relationship depends on the effort that each expends. Suppose that individual i's utility from the relationship is x² + x; − xixj, where x¿ is individual i 's effort and x ; is the effort of the other person (i = 1, 2). Assume x1, x2 ≥ 0. Which statement is true? There is a Nash equilibrium in which each player chooses effort level k > 0. This equilibrium is Pareto efficient. There is no mixed-strategy Nash equilibrium. There is a unique Nash equilibrium in which each player chooses no effort x¿ = x; = 0. The set of Nash equilibria in this game is finite. There is a Nash equilibrium in which xi = 0 and x ; = 1| =
Consider two players, designated by i = 1,2, involved in a dynamic bargaining over a perfectly divisible surplus of size 1. At the beginning of the interaction (at timet 1), player 1 chooses x1 in [0, 1]. Player 2 observes this offer and decides whether or not to accept it. If player 2 accepts this offer, the game ends and the utilities of player 1 and 2 equal x1 and 1- x1, respectively. If player 2 does not accept this offer, the game goes into the second round with a probability of \pi = 2|1/2-x11, while with probability 1 -\ pi the game ends and both players get a payoff of 0. If the game reaches the second round, t = 2, player 2 makes a counter-offer x2 in [0, 1] observing the whole past. Player 1 sees this offer and decides whether or not to accept it. If player 1 accepts x2, then the game ends and player 1 gets a payoff of x2 and player 2 a utility of 1 - x2. Both players get a payoff of zero when player 1 rejects player 2's offer x2 and the game ends. We assume that the game is…
Consider two consumers (1; 2), each with income M to allocate between two goods. Good 1 provides 1 unit of consumption to its purchaser and units of consumption to the other consumer. Each consumer i, i = 1; 2, has the utility function is consumption of good 1 and is consumption of good 2. a. Provide an interpretation of α. b. Suppose that good 2 is a private good. Find the Nash equilibrium levels of consumption when both goods have a price of 1. c. By maximizing the sum of utilities, show that the equilibrium is Pareto-ancient if α = 0 but incident for all other values of α. d. Now suppose that good 2 also provides 1 unit of consumption to its purchaser and a, 0 ≤ α ≤ 1, units of consumption to the other consumer. For the same preferences, find the Nash equilibrium and show that it is ancient for all values of α. e. Explain the conclusion in part d.
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Consider the game in the image attached below, which is infinitely repeated at t = 1, 2, ... Both players discount the future at rate: delta E (0, 1). The stage game is in the image attached. "Grim Trigger" strategies: Describe the "Grim Trigger" strategy profile of this game. Draw the finite automata representation of this strategy profile. Find the lowest value of delta for this strategy profile to form a subgame perfect equilibrium.
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200- 100- 66.7-- 50- a B's best response 50 100 66.7 B) 50 pizzas. A's best response C) 25 pizzas. The above figure shows the reaction functions for two pizza shops in a small isolated town. The Stackelberg leader will produce A) 100 pizzas. 200 D) 66.7 pizzas. 4p S E
Consider the utility function of U(X,Y) = ΧΛΟ.2YΛΟ.4 Show that Slutsky equation holds Show that ex,px+ex,py+ex,l=0. What does it mean? Show that Engle Aggregation holds. What does it mean? Show that Cournot Aggregation holds. What does it mean?