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The Anscombe and Aumann derivation of subjective expected utility relies on the set of states of nature S being finite. How would we extend it to infinite state spaces? This problem takes you (step by step) through one extension that, essentially, adapts the original proof. There is a lot of setup and notation involved, so if you tackle this, please be patient. First, we provide a setup. Begin with an arbitrary state space S and an arbitrary prize space X. As in the text, let Π be the space of simple probability distributions on X. The setup also involves an algebra of subsets of S, denoted A; an algebra ofsubsets is a set ofsubsets such that (1) S ∈ A (2) if A ∈ A , then the complement of A, denoted A C, is also ∈A and (3) if A, B ∈ S then A ∩ B ∈ A (If you've never worked with this concept before, you might want to prove: If A has properties (1) through (3), then A is also closed under unions.)
We can analyze the motion in each coordinate direction independently,integrating the acceleration to determine the velocity and then integrating the velocity to determine the position.
Draw his budget constraint line. What is his opportunity set?
How to find equilibrium GDP with various tax rates How do put these equations together to figure this outGovernment purchases, taxes and net exports are all zero.
Suppose that the demand for and supply of bonds both change with the state of the business cycle. In economic expansions, the demand for bonds is given by the equation D = 200 + 2,000r and the supply of bonds is S = 500 - 1,000r.
In fact, he has operated this livestock operation for over 20 years. in the past, his farm was fairly isolated. however more recently the nearest city, woodpile, has been expanding. thus, there are now residential homes fairly close to Brain's far..
In trip calculation, it is observed that a Wal-Mart store driver successfully made a total of 104 trips in a given period of time. During field calculation, it is shown that the calculated number of trips is actually 128. What is the value of the ..
Suppose a car wash firm that has 3 workers is able to wash 120 cars per day. When it adds one more worker, it is able to wash 152 cars per day in total. Suppose each car wash costs $15. Then the marginal revenue product for the 4th worker is
What parts of the continental United States today were not part of the U.S. in 1783? What countries claimed these lands (specify which country claimed which part) beyond U.S. borders in 1801?
Predict the new equilibrium price, and illustrate with a graph. (Related to Application 4 on page 673.)
Consider an economy in which there are 50 people, who consume a private good (bread) and a public good (circuses). There are, however, two types of people (type 1 and type 2).
In discussion of business and society. Why is there a tendency to focus on large firms rather than small or medium-sized firms? Have the corporate ethics scandal of the past decade affected small- and medium-sized firm? If so, in what ways have th..
Just prior to signing the contract, a manager reads that one of TRW's competitors has introduced a comparable airbag using a new technology that reduces the cost by 30%. How would this information affect Honda's optimal contract length with TRW
An interesting application of supply and demand to addictive substances compares alternative techniques for supply restriction. For this problem, assume that the demand for addictive substances is inelastic.
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