5. Mixed Strategy (20 points)
Consider a patent race game in which a “weak” firm is given an endowment of 4 and a “strong” firm is given an endowment of 5, and any integral amount of the endowment could be invested in a project. That is, the weak firm has five pure strategies (invest 0, 1, 2, 3 or 4) and the strong firm has six (0, 1, 2, 3, 4 or 5). The winner of the patent race receives the return of 10. Both players are instructed that whichever player invests the most will win the race and if there is a tie, both lose: neither gets the return of 10.
Lesson-No. Date Japanese English
Lesson65 緑 2日 今日 私 夏休 い 話し す Today, I'm going to talk about my summer vacation. Lesson66 緑 3日 私 父 釣 行 し 大 魚 釣 し I went fishing with my dad. I caught a big fish.
Lesson67 緑 4日 視線 合わせ 大 声 話し し う Make eye contact and speak in a loud voice. Lesson68 緑 5日 私 京都 楽し し I had a lot of fun in Kyoto.
(a) BR i (x j ) = 0 if x j > 0 and any non-negative number if x j = 0. So, there
is a unique Nash equilibrium, (0, 0). This equilibrium is not Pareto efficient. If both players choose strictly positive effort k(> 0), then the payoff of each player becomes k 2 + k − k 2 = k, which exceeds the Nash equilibrium payoff 0.
Problem Set 2: Posted on November 4
Advanced Microeconomics I (Fall, 1st, 2014)
1. Question 1 (7 points)
A real-valued function f (x) is called homothetic if f (x) = g(h(x)) where g : R → R is a strictly increasing function and h is a real-valued function which is homo- geneous of degree 1. Suppose that preferences can be represented by a homothetic utility function. Then, prove the following statements.
Let w = (w 1 , w 2 , w 3 , w 4 ) ≫ 0 be factor prices and y be an (target) output.
(a) Does the production function exhibit increasing, constant or decreasing returns to scale? Explain.
(b) Calculate the conditional input demand function for factors 1 and 2. (c) Suppose w 3 >
How to Measure Welfare Change | 厚生の変化をどうはかるか？
When the economic environment or market outcome changes, a consumer may be made better off ( 改善 ) or worse off ( 悪化 ). Economists often want to measure how consumers are affected by these changes, and have developed several tools for the assessment of welfare ( 厚生 ).
Constant Absolute Risk Aversion
Def We say that preference relation % exhibits invariance to
wealth if (x + p 1 ) % (x + p 2 ) is true or false independent of x.
Thm If u is a vNM continuous utility function representing preferences that are monotonic and exhibit both risk aversion and invariance to wealth, then u must be exponential,