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Econ 3332
Intermediate Microeconomics
Professor Scott Imberman
Problem Set 4
1)
Bernheim & Whinston, pg. 323, exercise 9.8
If Dan produces, he will choose a quantity that satisfies the quantity rule:
P = MC
P = 4 + (Q/20)
P – 4 = Q/20
20P – 80 = Q
Dan will only produce, however, if the price is higher than the minimum of average
cost. Since cost is C(Q) = 4Q + (Q
2
/40), then AC(Q), which is just C(Q)/Q must be 4
+ (Q/40). Just from looking at the function, we can tell that the minimum of AC(Q)
occurs at a quantity of zero (or just about zero) and that the minimum AC(Q) is $4.
Therefore, Dan will produce at any price greater than or equal to $4, and his supply
function is:
S(P) =
0i
f
$
20
80 if
$4
P
PP
⎧⎫
<
⎪⎪
⎨⎬
−≥
⎩⎭
4
5
If Dan has an avoidable fixed cost of $10, then his cost function for producing
becomes C(Q) = 4Q + (Q
2
/40) + 10, and his average cost becomes 4 + (Q/40) +
(10/Q). To find the minimum of this AC(Q) function, we have to set it equal to MC(Q).
AC(Q) = MC(Q)
4 + (Q/40) + (10/Q) = 4 + (Q/20)
(Q/40) + (10/Q) = (Q/20)
(10/Q) = (Q/40)
Q
2
= 400
Q = 20
We can then see that AC(20) = MC(20) = $5. This means that Dan will only produce
in this case if the price is greater than or equal to $5. If he does produce, he still uses
the same condition as above, so his supply function would be:
S(P) =
f
$
20
80 if
$5
P
<
2)
Bernheim & Whinston, pg. 401, exercise 11.3.
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View Full DocumentWe know that expected consumption at point A is 500.
Therefore we need to figure
out some points using the probabilities provided where expected consumption is the
same.
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 Spring '08
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 Microeconomics

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