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*Show that the monotone likelihood ratio condition (f(x)/g(x) increasing in x,
where x is a real number) implies first-order stochastic dominance (F(x) £ G(x) for
all x).
Let q = q1 or q2 denote the state of nature in a two state world. Let p0 = Pr(q = q1).
Let f(p) be an arbitrary distribution on the unit interval such that òpf(p)dp = p0.
Show that f(p) can be construed as a distribution over posterior probabilities of p,
stemming from an experiment with outcomes y, a prior probability p = p0 and two
likelihood functions p(y|q1) and p(y|q2). [It may be easier to solve the problem if
you assume that f(p) consists of two mass points so that the experiment will have
only two relevant outcomes, say, yL and yH.]
An agent has to decide between two actions a1 and a2, uncertain of the prevailing
state of nature s, which can be either s1 or s2. The agent’s payoff as a function of the
action and the state of nature is as follows:](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
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🌐 Global Perspective - Economics is a global discipline, and we'll explore economic issues from around the world. Whether it's the economic implications of a global event or regional economic disparities, we've got it covered.
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- 2. economicshomeworkhelper.com *Show that the monotone likelihood ratio condition (f(x)/g(x) increasing in x, where x is a real number) implies first-order stochastic dominance (F(x) £ G(x) for all x). Let q = q1 or q2 denote the state of nature in a two state world. Let p0 = Pr(q = q1). Let f(p) be an arbitrary distribution on the unit interval such that òpf(p)dp = p0. Show that f(p) can be construed as a distribution over posterior probabilities of p, stemming from an experiment with outcomes y, a prior probability p = p0 and two likelihood functions p(y|q1) and p(y|q2). [It may be easier to solve the problem if you assume that f(p) consists of two mass points so that the experiment will have only two relevant outcomes, say, yL and yH.] An agent has to decide between two actions a1 and a2, uncertain of the prevailing state of nature s, which can be either s1 or s2. The agent’s payoff as a function of the action and the state of nature is as follows:
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