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Homework 1  Solutions
Evrim Dener
Eco 4382  Fall 2007
1) (a) Q=53P
Inverse demand P=53Q
TR=PQ
TR=(53Q)Q
MR=dTR/dQ=532Q
MR=MC
532Q=5
Q*=24, P*=53Q*=29
*=(P*AC)Q*=(295)24=576
(b) P=MC
53Q=5
Q*=48
(c)
(d) CS shrank from ADF to ABC
PS increased by BCDE
DWL is CEF
1
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View Full Document2) 2.8) (a) Total Revenue is given by p(
Q
) .
Q
, that is, the revenue that
LasOVision receives when it sells
Q
units. To get p(
Q
), we invert the demand
function
Q
= 10,200  lOOp by solving for p in terms of
Q
, or
p
(
Q
) = 102
Q=
100
:
Substituting this into our total revenue equation, we obtain
TR
(
Q
) =
(102
Q=
100)
Q
= 102
Q
Q
2
=
100
:
(b) Marginal revenue is the derivative of Total Revenue with respect to
Q
,
so MR (
Q
) = 102
Q
/50; or, since our demand equation is linear in
Q
, we can
obtain it by recalling that the marginal revenue curve is twice as steep as the
inverse demand curve and starts at the same point on the vertical axis.
Q
* is that quantity at which marginal
cost and marginal revenue are equal. Setting MR(
Q
) = MC ,we have 102 
Q
*/50
=
Q
*, or
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 Spring '08
 Dener
 Economics

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