Applied Mathematics for Business and Economics

Lecture Note Function

market price at which supply equals demand. We can say another way that the market
price is a price at which there will be neither a surplus nor a shortage of the commodity.

Example 5
Find the equilibrium price and the corresponding number of units supplied and
demanded if the supply function for a certain commodity is Sp p( )=^2 +− 37 p 0 and

the demand function isDp()=− 410 p.

Solution
Set Sp()equal to Dp() and solve for p to get

()()

2

2

3 70 140

4 480 0

20 24 0

20 or 24

p pp

pp

pp

pp

+ −= −

+− =

−+=

==−

Hence we conclude that the equilibrium price is $20. Since the corresponding supply and
demand are equal, we use the simpler demand equation to compute this quantity to get

D( (^20) )=−=410 20 390
Hence, 390 units are supplied and demanded when the market is in equilibrium.
Exercises
1 cUrKNnatémøGnuKmn_eTAtamkarbBa¢ak;dUcxageRkam (Compute the indicated values of the
given function)
a. fx()=+−352;1,0, 2x^2 x f( ) f( ) f(−)
b. () ()()()

1

gx x ;1,1,2g g g

x

=+ −

c. ht()=++t^2 24,2,0, 4t h() () ( )h h−

d. () ( ) () () ( )

32

ft 21 ; 1, 5, 13t f f f

−

=−

e. ()

3if

1if5 5

if 5

t

tt t

tt

⎧ <−

⎪

=+ −≤≤⎨

⎪

⎩ >

f ; fff(−−6,) ( 5, 16) ( )

2 cUrbBa¢ak;GMBIEdnkMNt;rbs;GnuKmn_dUcxageRkam(Specify the domain of the given function)

a. ()

(^21)
2
x
gx
x

+

=

+

b.yx= − 5 c.gt()= t^2 + 9

d. () ( )

32

ft=− 24 t e. ()( )

2 12

fx x 9

−

=−^

3 ]bmafaéføedImsrubKitCaduløaelIkarplitTMnijmYyRbePT cMnYn ÉktaRtUvkMNt;edayGnuKmn_

.

q

Cq q()=− + +^3230 q 400 q 500

k> KNnaéføedImelIkarplitcMnYn 20Ékta.

x> KNnaéføedImelIkarplitÉktaTI20.