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

  1. Plot the demand supply and curve.

When QS is 0, P is 0.

When QD is 0, P is $5

P ($)

S

Q

D

  1. What are the equilibrium price and equilibrium quantity for the industry? Determine the answer in algebraically and graphically.

P ($)

S

Q

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 = 65,00010,000PQS = -35,000 + 15,000 P

Where Q is the quantity and P is the price of a poster, in dollar.

  1. 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
  1. 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.

  1. At what average monthly fee would demand equal zero?

QD = 3000-10P

3000-10P = 0

10P = 3000

P=$300

  1. At what average monthly fee would supply equal zero?

QS = -1000+10P

-1000+10P = 0

10P = 1000

P=$100

  1. Plot the supply and demand curve.

P ($)

S

Q

D

  1. What is the equilibrium price/output level?

QD = QS

3000 –10P = -1000+ 10P

4000 = 20P

P = $200

  1. 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 ($), Pop is pollution, I is disposable income per household (S), and A is advertising expenditure ($).

  1. Determine the demand curve for the company in a market in which

P = 300 Pop = 1,000,000I = 30,000A = 15,000

Q = 10,000 ̶ 200 (300) +0.03 (1,000,000) +0.6 (30,000)+ 0.2 (15,000)

Q = 1000

  1. 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

  1. 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 analysisof 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.

  1. 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

  1. 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

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.