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aps4x313_s06

aps4x313_s06 - Econ 313 Wissink Spring 2006 PS#4 XtraQ...

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1. There is a 50-50 chance that an individual with utility u=√(\$) and with wealth of \$20,000 will contract a debilitating disease and suffer a loss of \$10,000. a. \$expected value = .5*20,000 + .5*10,000 = \$15,000. b. the expected utility = .5*√20,000 + .5*√10,000 = .5*141.42 + .5*100 = 120.71 utils c. the \$certainty equivalent = 120.71 2 = \$14,571 d. Set Wgood=Wbad=\$CE=\$14,571. So 14571=20000-Prem Prem = \$5429. And then, 14571=20000-10000-5429+Ben Ben = \$10,000. Expected profit = 5429-(.5*10000)=\$429 e. \$expected value = .25*20,000 + .75*10,000 = \$12,500. expected utility = .25*√20,000 + .75*√10,000 = .25*141.42 + .75*100 = 110.36 utils \$certainty equivalent = 110.36 2 = \$12,179 Wgood=Wbad=\$CE=\$12,179. So 12179=20000-Prem Prem = \$7821. And then, 12179=20000-10000-7821+Ben Ben = \$10,000 Expected profit = 7821-(.75*10000)=\$321 2. Diminishing returns to scale implies that if x=f(L,K) and y=f(sL, sK) where s>1, then y<sx. All inputs must be scaled by the same factor, s, in the concept of returns to scale . With diminishing returns to a factor of production, look at how the marginal product of a factor varies, holding the other factors constant. The concept of diminishing returns to a factor of production implies that eventually the marginal product of the factor declines.

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