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Supply and Demand Problems
1) Q=2000 - 100 P, where Q is cap sales and P is price.
A. how many caps could be sold at $ 12 each?
Q = 2000-100(12)
Q = 800 caps
B. what should the price be in order the company to sell 1000 caps?
1000 =2000 - 100 P
100 P = 1000
P=$10
C. at what price would cap sales equal o zero?
Q =2000-200 P
2000-200 P =0
P = $20
2) Consider the following supply and demand curves for a certain product.
QS = 25,000P
QD = 50,000- 10,000P
a. Plot the demand supply and curve.
When QS is 0, P is 0.
When QD is 0, P is $5
P ($)
S
5
Q
D
b. What are the equilibrium price and equilibrium quantity for the industry?
Determine the answer in algebraically and graphically.
P ($)
S
5
1.43
Q
D
QS = QD
25,000P = 50,000- 10,000P
50,000 = 35,000 P
P = $1.43
When P = $1.43, QD = 50,000- 10,000(1.43)
QD = 35700
Thus equilibrium price is $1.43 while equilibrium quantity is 35700 units
3) QD = 65,000 −10,000P
QS = -35,000 + 15,000 P
Where Q is the quantity and P is the price of a poster, in dollar.
a. Complete the following table.
Price
QS
QD
Surplus or shortage
$ 6.00
55,000
5000
surplus
5.00
40,000
15,000
Surplus
4.00
25,000
25,000
equilibrium
3.00
10,000
35,000
Shortage
2.00
-5000
45,000
Shortage
1.00
-20,000
55,000
shortage
b. What is the equilibrium price?
QD = QS. Thus, Price is $ 4.00
4) The following relations describe monthly demand and supply for computer
support service catering to small business.
QD = 3,000 – 10P
QS = -1,000 + 10P
Where Q is number businesses that need services and P is the monthly fee, in
dollar.
a. At what average monthly fee would demand equal zero?
QD = 3000-10P
3000-10P = 0
10P = 3000
P=$300
b. At what average monthly fee would supply equal zero?
QS = -1000+10P
-1000+10P = 0
10P = 1000
P=$100
c. Plot the supply and demand curve.
P ($)
S
300
200
100
Q
D
d. What is the equilibrium price/output level?
QD = QS
3000 –10P = -1000+ 10P
4000 = 20P
P = $200
e. Suppose demand increase and leads to new demand curve:
QD = 3500 ̶ 10P
What is the effect on supply? What are the new equilibrium P & Q?
When demand increase, supply will increase.
QD = 3500- 10P, When QD is 0, P is $350
QS= -1500+10P, When QS is 0, P is $150
Thus, new equilibrium P & Q is $250
5) The ABC marketing consulting firm found that a particular brand of portable
stereo has the following demand curve for a certain region:
Q = 10,000 ̶ 200 P +0.03Pop +0.6 I + 0.2A
Where Q is the quantity per month, P is price ($), Pop is pollution, I is
disposable income per household (S), and A is advertising expenditure ($).
a. Determine the demand curve for the company in a market in which
P = 300 Pop = 1,000,000 I = 30,000 A = 15,000
Q = 10,000 ̶ 200 (300) +0.03 (1,000,000) +0.6 (30,000) + 0.2 (15,000)
Q = 1000
b. Calculate quantity demanded at prices of $200, $175, $150 and $125.
At $200;
Q = 10,000 ̶ 200 (200) +0.03 (1,000,000) +0.6 (30,000) + 0.2 (15,000)
Q = 21,000
At $175;
Q = 10,000 ̶ 200 (175) +0.03 (1,000,000) +0.6 (30,000) + 0.2 (15,000)
Q = 26,000
At $150;
Q = 10,000 ̶ 200 (150) +0.03 (1,000,000) +0.6 (30,000) + 0.2 (15,000)
Q = 30,000
At $125;
Q = 10,000 ̶ 200 (125) +0.03 (1,000,000) +0.6 (30,000) + 0.2 (15,000)
Q = 36,000
c. Calculate the price necessary to sell 45,000 units.
45,000 = 10,000 ̶ 200 P +0.03 (1,000,000) +0.6 (30,000) + 0.2 (15,000)
45,000 = 61,000 ̶ 200 P
P = $80
6) Joy’s Frozen Yogurt shops have enjoyed rapid growth in northeastern. States
in recent years. From the analysis of joy’s various outlets, it was found that
the demand curve follows this pattern:
Q = 200 – 300P + 120I + 65T – 250AC + 400 Aj
Where Q = Number of cups served per week
P = average price paid for each cup
I = Per capita income in the given market (thousands)
T = Average outdoor temperature
AC = Competition’s monthly advertising expenditures (thousands)
Aj = Joy’s own monthly advertising expenditure (thousands)
One of the outlets has the following conditions: P = 1.50, I = 10, T= 60, AC
= 1.5, Aj = 10.
a. Estimate the number of cups served per week by this outlet. Also
determine the outlet’s demand curve.
Q = 200- 300 (1.50) + 120 (10) + 65(60) – 250(15) + 400 (10)
= 5100
5100 = 200 – 300(1.50) + 120 (10) + 65 (60) – 250 (15) + 400(10)
5100 = 200 – 300P + 1200 +3900 – 3750 + 400
= 200 – 300P + 1750
300P = 200 + 1750 – 5100
P = -10.5
P
1.5
Q
5100
b. What would be the effect of a $5,000 increase in competitor’s advertising
expenditure? Illustrate the effect on the outlet’s demand curve.
Q
= 200 – 300 (1.50) + 120 (10) + 65 (60) – 250 (5015) + 400 (10)
= -1244900
P
1.5
Q
-1244900
9) Q=1000-3000P+10A
When P=$3 and A=$2000, Q=1000-3000(3) +10(2000) =12000
When P=$2.50 and A=$2000, Q=1000-3000(2.50) +10(2000) = 13500.
Thus, it beneficial, because higher quantity demanded
When P=$4 and A=$2100
Q=1000-3000(4) +10(2100) = 10000.
Thus, it is not beneficial, because lower quantity demanded.