Lecture Note Differentiation
]bmafasmIkartRmUvkarénmuxTMnijmYyRbePTkMNt;edayqp=−200 2^2 ¬cMeBaH 010 ≤≤p ¦.
k> cUrsresrkenSameGLasÞicéntRmUvkarCaGnuKmn_nwgp. x> KNnaeGLasÞicéntRmUvkar eB
rYcbkRsaylT§pl. K> etIéføesμIb:unμ μIeTAnwg
5
of unit elasticity with
b. esults from part a. to determine the intervals of increase and
h revenue is
and use its fi vative to
e
]bmaf
l
p= (^6) aneTIbeGLasÞicéntRmUvkar es െ1?
41 Suppose that the demand equation for a certain commodity is (for
0 ).
qp=−500 2
02 ≤≤p
a. Determine where the demand is elastic, inelastic, and
respect to price.
Use the r
decrease of the revenue function and the price at w ich
maximized.
c. Find the total revenue function explicitly rst deri
determine its intervals of increase and decrease and price at which revenu
is maximized.
asmIkartRmUvkarénmuxTMnijmYyRbePTkMNt;edayqp=500 2− ¬cMeBaH 02 ≤≤p 50 ¦.
;eday
uKmn_man
42
k>cUrrkcenøaHEdlenAkñúgenaH tRmUvkarmanPaBeGLasÞic mineGLasÞic nigeGLasÞicÉktaeFob
eTAnwgéfø. x>eRbIlT§plrbs;sMNYrk> cUrrkcenøaHEdlGnuKmn_R)ak;cMNUlekIneLIg nigfycuH
RBmTaMéfø EdleFVI[GnuKmn_R)ak;cMNUlmantémøGtibrma. K> cUrrkGnuKn_R)ak;cMNUldac
ELk rYceRbIedrIevTI1rbs;vaedim,IrkcenøaHEdlvaekIn nigcuH RBmTaMgéføEdleFVI[Gn
Gtibma.
Suppose that the demand equation for a certain commodity is qp=−120 0.1^2 for
( 0 ≤≤p 1, 200)
a. Determine where the demand is elastic, in of unit ith
respect to price.
b. Use the results of part a. to determine the intervals of increase and
decrease of the revenue function and the price at which revenue is
maximized.
c. Find the total revenue function explicitly and use its first derivative to
determine its intervals of increase and decrease and the price at which
rev
elastic, and elasticity w
enue is maximized. ]bmafasmIkartRmUvkarénmuxTMnijmYyRbePTkMNt;eday
qp=−120 0.1^2 ¬cMeBaH01,200≤≤p ¦.
k> cUrrkcenøaHEdlenAkñúgenaH tRmUvkarmanPaBeGLasÞic mineGLasÞic nigeGLasÞicÉktaeFob
eTAn
RBm dac;eday
ELk rYceRbIedrIevTI1rbs;vaedim,IrkcenøaHEdlvaekIn nigcuH RBmTaMgéføEdleFVI[GnuKmn_man
Gtib
43 Suppo
equati
wgéfø. x>eRbIlT§plrbs;sMNYrk> cUrrkcenøaHEdlGnuKmn_R)ak;cMNUlekIneLIg nigfycuH
TaMéfø EdleFVI[GnuKmn_R)ak;cMNUlmantémøGtibrma. K> cUrrkGnuKn_R)ak;cMNUl
ma.
se the demand q and price p for a certain commodity are related by the
on p=−60 2qfor ( 030 ≤q≤ )
a. Express the elasticity of demand as a function of q.