(b) Now suppose there are n(> 2) individuals. Then, can we find a competitive equilibrium? (How) Does your answer depend on n?
4. Question 4 (8 points)
Consider a production economy with two individuals, Ann (A) and Bob (B), and two goods, leisure x 1 and a consumption good x 2 . Ann and Bob have equal en-
payoff) while M gives 1 irrespective of player 1’s strategy.
Therefore, M is eliminated by mixing L and R .
After eliminating M , we can further eliminate D (step 2) and L
(step 3), eventually picks up ( U , R ) as a unique outcome.
4.2 Linear preferences
Throughout the analysis, we have restricted our attention to a model with quadratic prefer- ences where the utility loss is quadratic in the distance from the bliss point. We focus on this specification because it is perhaps the most commonly used setup in applications. The focus on the quadratic specification also facilitates comparison with previous works, many of which build on this specification. There is a drawback, however, as the quadratic specification necessarily entails the risk effect that happens to work in the same direction as the confirmation effect and somewhat obscures the extent of the confirmation effect – the novel feature of our model – as a consequence.
u(x, y) = x 2
+ y 2
(ω x , ω y ) = (1, 1)
(a) Assume there are only two individuals in this economy. Then, draw the Edgworth-box and show the contract curve. Find a competitive equilibrium if it exists. If there is no equilibrium, explain the reason.
her whole pitch range.
Let us now move on to the next speaker. Figure 6 shows the intonational contours of the tsun, moe and normal voice of Speaker 2. As was the case for Speaker 1, the moe voice is generally higher than the normal voice, and the tsun voice is lower than the normal voice. Unlike Speaker 1, we observe clear separations be- tween the three voice types in the L-tones (normal vs. tsun: t = −4.38, p < .001; normal vs. moe: t = 15.31, p < .001). Nevertheless, we observe larger sep- arations in the patterning of H-tones (normal vs. tsun: − 9.08, p < .001; normal vs. moe: t = 24.0, p < .001.). A Brown–Forsythe test shows that H-tones show more variability than L-tones (F(1, 640) = 129.41, p < .001), indicating that this speaker, too, manipulates H-tone targets more than L-tone targets to express different speech styles 4) . We may be able to consider this pattern
St Petersburg Paradox | セントペテルスブルグのパラドックス (2) The St Petersburg paradox shows that maximizing your dollar expectation may not always be a good idea. It suggests that an agent in risky situation might want to maximize the expectation of some “utility function” with decreasing marginal utility:
No strategy looks to be dominated…
If a player 2 randomizes L and R with 50% each, then
Such mixed (randomized) strategy yields 1.5 (as an expected payoff) while M gives 1 irrespective of player 1’s strategy.