1.
There is a 5050 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=20000Prem
Prem = $5429.
And then,
14571=20000100005429+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=20000Prem
Prem = $7821.
And then,
12179=20000100007821+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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 Fall '06
 MASSON
 Economics, Utility, Marginal product, Economics of production, APL

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