a) Consider a set of monetary outcomes X ={x1, ... , xK} where the outcomes are arrangedin increasing order x, << XK. Let p and q be simple lotteries. We say that lottery p•..first-order stochastically dominates lottery q, if the following holds:KKE p(x;) > E qcx,)j=ij=iwith at least one of the inequalities being strict. Explain the intuition of first-order stochas-tic dominance. Show that, for expected utility preferences with vNM utility u that is strictlyincreasing in money, if p first-order stochastically dominates q then p > q.

a) Consider a set of monetary outcomes X {x1, ... , Xg} where the outcomes are arranged in increasing order x, < .… < xK. Let p and q be simple lotteries. We say that lottery p first-order stochastically dominates lottery q, if the following holds: K K E P(x,) > E q(x,) for all i = 1, ... K, j=i j=i

a) Consider a set of monetary outcomes X {x1, ... , Xg} where the outcomes are arranged in increasing order x, < .… < xK. Let p and q be simple lotteries. We say that lottery p first-order stochastically dominates lottery q, if the following holds: K K E P(x,) > E q(x,) for all i = 1, ... K, j=i j=i

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

a) Consider a set of monetary outcomes X = {x1,... , Xk} where the outcomes are arranged in increasing order x, g(x;) for all i = 1,... K, j=i j=i with at least one of the inequalities being strict. Explain the intuition of first-order stochas- tic dominance. Show that, for expected utility preferences with vNM utility u that is strictly increasing in money, if p first-order stochastically dominates q then p > q.
Assume that two collectors, X and Y are in a first prize sealed bid auction for a batch of vintage comic books. X and Y have different valuations (V) for this batch of comic books e.g. VX And VB are between $2000 and $4000. Both collectors know their own V but does not know the V of the other collector. All they know is that the other collector’s V is a uniformly distributed number between $2000 and $4000. Assume risk neutrality for X and Y e.g. expected payoff for X is: (VX – bX)Pr(bX) and expected payoff for Y is (VY – bY)Pr(bY). These collectors will make their bids strategically. Show how X’s bidding strategy is bX = ½ Vx + 1 and Y’s is bY = ½ Vy +1 in a Nash equilibrium.
Apple and Google are interested in hiring a new CEO. Both firms have the same set of final candidates for the CEO position: Indra, Cao, and Virginia. Both firms need to decide who to make a job offer to, and the hiring process is such that they each only make one job offer. If, say, Apple makes a job offer to Indra and Google makes a job offer to one of the other candidates, then Apple’s probability of success in hiring Indra is pIndra. The same is true for Google. If they both make a job offer to Indra, each has probability pIndra/2 of success. It has been estimated that pIndra = 20%, and pCao = pVirginia = 30% (Note that these probabilities need not add up to 100%). Suppose that both Apple and Google attach a valuation of 10 to successfully hiring Indra, and a valuation of 7 to successfully hiring each of the other candidates. A hiring attempt, if unsuccessful, has a valuation of zero. Convert this story into a game by completing the following game table; Google…
Exercise 1.8. Consider the following "third-price" auction. There are n≥ 3 bidders. A single object is auctioned and Player / values the object $v,, with V, > 0. The bids are simultaneous and secret. The utility of Player / is: 0 if she does not win and (v-p) if she wins and pays $p. Every non-negative number is an admissible bid. Let b, denote the bid of Player i. The winner is the highest bidder. In case of ties the bidder with the lowest index among those who submitted the highest bid wins (e.g. if the highest bid is $120 and it is submitted by players 6, 12 and 15, then the winner is Player 6). The losers don't get anything and don't pay anything. The winner gets the object and pays the third highest bid, which is defined as follows. Let be the winner and fix a Player j such that b₁ = max({b,,...,b,}\ {b}) [if GAME THEORY - Giacomo Bonanno 39 max({b,...,b}\{b;}) contains more than one element, then we pick one of them]. Then the third price is defined as max({b₁,...,b}\{b,,b;}).…
a) Consider a set of monetary outcomes X = {x1,...,Xk} where the outcomes are arranged in increasing order x, E q(x,) for all i = 1, ... K, j=i j=i with at least one of the inequalities being strict. Explain the intuition of first-order stochas- tic dominance. Show that, for expected utility preferences with vNM utility u that is strictly increasing in money, if p first-order stochastically dominates q then p > q.
Let A be an m x n matrix representing the payoff of n securities in m states of the world. If the market is complete, which of the following statements are true? Provide counter examples in case not. (a) A is of full rank (b) A is invertible (c) The prices of n securities are free of arbitrage
State the Gauss-Markov Theorem.
Why do sellers generally prefer a Vickrey auction to a regular sealed bid if sellers don’t receive the highest bid in the Vickrey auction? Sellers only have to sell their item if the bid is the highest-price bid. The second-highest bid in a Vickrey auction is generally higher than the highest bid in a regular sealed-bid auction. The second-highest bid is about the same in both auctions. Sellers prefer the final price is not revealed to all bidders. Sellers would never prefer Vickrey auctions.
As the manager of Smith Construction, you need to make a decision on the number of homes to build in a new residential area where you are the only builder. Unfortunately, you must build the homes before you learn how strong demand is for homes in this large neighborhood. There is a 60 percent chance of low demand and a 40 percent chance of high demand. The corresponding (inverse) demand functions for these two scenarios are P = 400,000-400Q and P=900,000-2500, respectively. Your cost function is C(Q)=125,000+ 430,0000. How many new homes should you build, and what profits can you expect? Number of homes you should build: homes
Consider the version of the Beauty Contest game from the class, in which the players are trying to guess the average guess minus one. More precisely, the utilities now are: ui (si; sj ) = -|si-(-1)| where sj/#l forj belong tI (a) Which strategies are strictly dominated in this game, and by which alternative strategies? And so, what is the set of strategies BR11 (b) What is the set BR21 ? What is the set BRni for any n > 0?
Consider the following model about the auctions. We have two buyers each obtain a private signal about the value of good being auctioned. The signal can be either high (H) or low (L) with equal probability. If both obtain signal H, the good is worth 1; otherwise, it is worth 0.a. What is the expected value of the good1 to a buyer who sees signal L and to a buyer who sees signal H?b. Suppose buyers bid their expected value computed in part (a). Show that they earn negative profit conditional on observing signal H.
Consider the following game, with a risk-neutral principal with preferences π = q - w hiring an agent with preferences U = √w-e.. The agent's reservation utility is given by Ū = 2, and the agent can choose between an effort level of 0 or an effort level of 10. Output is either 0 or 400 and follows the following probability distribution, a function of effort level and some uncertain factor: e=0 e=10 Probability (q=0) Probability (q=400) 0.6 0.4 0.9 0.1 What would the contract look like if the principal tried to push the wages when q=0 to zero? Would the principal want to do this? Explain.