Applied Mathematics for Business and Economics

Lecture Note Differentiation

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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

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l

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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

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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.