4 1 market-equilibrium

4.1 Market Equilibrium4.1 Market Equilibrium

Market Equilibrium


• Demand – quantities of a commodity sold or expected to be sold

• Supply – quantities of a product producers are willing and able to sell

• Demand function: yD = D(x)

• Supply function: yS = S(x)

• Examples:

€

D(x) = −3x + 54

€

3x + 2yD −1,500 = 0

€

x = −0.3 + 8yS

€

S(x) =10 + 0.5x


• Law of Demand: There is a negative, or inverse, relationship between price and the quantity of a good demanded and its price.

• That is, as price decreases, quantity demand increases, and as price increases, quantity demand decreases.

• Demand curves slope downward.


• Law of Supply: There is a positive relationship between price and quantity of a good supplied.

• That is, the quantity supplied increases as the price increases, and quantity decreases correspondingly as the price decreases.

• Supply curves have positive slopes.


Example. The lowest price at which an office equipment is available in the market is Php7,200. When the price is Php8,500, buyers have 900 units available to them. Find the supply function assuming that it is linear.

€

(0,7200)

€

(900,8500)

€

y − 7,200 =8,500 − 7,200

900 − 0(x − 0)

€

y − 7,200 =1,300

900(x)

€

yS =13

9x + 7,200


Example. If the demand function is D(x) = –6x + 1,200,

a)what is the highest price anyone would be willing to pay for the commodity?

b)what is the quantity demanded if the commodity is given for free?

c) graph the demand curve.



a)what is the highest price anyone would be willing to pay for the commodity?

Highest price occurs when there is no demand for the commodity. That is, when x = 0.

€

D(0) = −6(0) +1,200

€

=Php1,200



b)what is the quantity demanded if the commodity is given for free?

If a commodity or product is free, D(x) = 0.

€

D(x) = −6x +1,200

€

0 = −6x +1,200

€

6x =1,200

€

x = 200



c) graph the demand curve.

Draw a line through (0,1200) and (200,0).

sage: plot(-6*x+1200,(0,220),xmin=0,ymin=0)


Market equilibrium – the condition that exists when the price that a consumer is willing to pay (D(x)) is equal to the price that a producer is willing to accept (S(x))

Equivalently, market equilibrium occurs when quantity supplied by a producer and quantity demanded by consumers are equal.€

S(x) = D(x)

€

xS = xD



• Shortage – occurs when quantity demanded exceeds quantity supplied at the current price

• Surplus – occurs when quantity supplied exceeds quantity demanded at the current price


1. Given the supply function S(x) = 10 + 0.5x and demand function D(x) = 100 – 0.5x, find the market equilibrium quantity and price.

€

S(x) = D(x)

€

10 + 0.5x =100 − 0.5x

€

x = 90

€

S(90) =10 + 0.5(90) = 55

€

. . m e quantity: 90 units

€

. . m e price: Php55


5. Given the supply function S(x) = 100 + 5x and demand function D(x) = 450 – 2x, find the market equilibrium quantity and price.

€

S(x) = D(x)

€

100 + 5x = 450 − 2x

€

x = 50

€

S(50) =100 + 5(50) = 350

€


€



7. Given the supply function yS – 4x – 92 = 0 and demand function yD + 5x – 200 = 0, find the market equilibrium quantity and price.

€

yS − 4x − 92 = 0 ⇒ yS = 4x + 92

€

yD + 5x − 200 = 0 ⇒ yD = −5x + 200

€

yS = yD

€

4x + 92 = −5x + 200

€

x =12

€

yS (12) = 4(12) + 92 =140

€


€



9. Given the supply function x = –11 + 0.5yS and demand function yD = 50 – 1.5x, find the market equilibrium quantity and price.

€

x = −11+ 0.5yS ⇒ yS = 2x + 22

€

yD = 50 −1.5x

€

yS = yD

€

2x + 22 = 50 −1.5x

€

x = 8

€

yD (8) = 50 −1.5(8) = 38

€


€



13. If the demand function is D(x) = –3x + 54,a)what is the highest price a consumer would

pay for the commodity?b)what is the quantity demanded if the

commodity is offered for free?c) draw the demand curve.


13. If the demand function is D(x) = –3x + 54,a)what is the highest price a consumer would

pay for the commodity?

Highest price occurs when x = 0.

€

D(0) = −3(0) + 54

€

=Php54


13. If the demand function is D(x) = –3x + 54,b)what is the quantity demanded if the

commodity is offered for free?

D(x) = 0 if the commodity is offered for free.

€

D(x) = −3x + 54

€

0 = −3x + 54

€

x =18


13. If the demand function is D(x) = –3x + 54,c) draw the demand curve.

sage: plot(-3*x+54,(0,20),xmin=0,ymin=0)


15. A manufacturer that produces a computer headset sells 400 units when the unit price is Php1,200. It has determined that with a Php80 reduction in the unit price, 120 more headsets will be sold. Find the demand function assuming that it is linear.

€

(400,1200)

€

(520,1120)

€

y −1,200 =1,120 −1,200

520 − 400(x − 400)

€

y −1,200 = −2

3(x − 400)

€

yD = −2

3x +

4,400

3


17. The lowest price an animation kit is supplied to the market is Php550. When the price is Php900 each, 200 kits are available in the market. Find the supply function.

€

(0,550)

€

(200,900)

€

y − 550 =900 − 550

200 − 0(x − 0)

€

y − 550 =7

4x

€

yS =7

4x + 550


23. The demand and supply functions of a computer accessory are D(x) = 4.5 – 2.5x and S(x) = 0.0375 + 0.125x, respectively. Find the market equilibrium point.

€

S(x) = D(x)

€

0.0375 + 0.125x = 4.5 − 2.5x

€

x =1.7

€

D(1.7) = 4.5 − 2.5(1.7) = 0.25

€

. . m e point: 1710 , 1

4( )


25. Suppose that the demand for video rentals per week is given by D(x) = 4.5 – 0. 25x and the supply of videos by the local video store per week is S(x) = –3 + 0. 5x. Calculate the equilibrium price and quantity in this market.

€

S(x) = D(x)

€

100 + 5x = 450 − 2x

€

x = 50

€

S(50) =100 + 5(50) = 350

€


Education

4 1 market-equilibrium