MANAGERIAL ECONOMICS: TUTORIAL #1

Presenters:Mr. XMrs. Y

QUESTION 1

The X-Corporation produces a good (called X) that is a normal good. Its competitor, Y- Corporation, makes a substitute good that it markets under the name “Y”. Good Y is an inferior good.

Income

Quantity of Good X

D1 D2

P2

P1

D2D1

• When income increases, the demand curve for normal goods shifts outward as more will be demanded at all prices.

• Since X is a normal good; an increase in income, indicates a right shift from D1 to D2

(a). How will the demand for good X change if consumer income increase?

Income

Quantity of Good X

D1 D2

P1

P2

D2D1

(b). How will the demand for Good Y change if consumer income decrease?

• An inferior good increase in demand when consumer income decrease.

• Since Y is a inferior good; a decrease in income, indicates a right shift from D1 to D2

(c). How will the demand for good X change if the price of good Y decreases?

• When the price of a substitute good Y decreases, the quantity demanded for good X also decreases. Therefore the demand curve for good X will shift to the left.

Price of Good Y

Quantity of Good X

D2 D1

P1

P2

D1D2

(d). Is good Y a lower-quality product than good X? Explain

• No. The term inferior good does not mean a lower-quality. It basically means that both income and demand are inversely related.

• For example; Car

QUESTION 2The demand for good X is given by:

Q = 1200 – Px/2 + Py/4 – 8Pz + M/10

Research shows that the prices of related goods are given by Py= $5,900 and Pz= $90, while the average income of individuals consuming this product is M= $55,000.

(a). Indicate whether goods Y and Z are substitutes or complements for good X.

Good Y is a substitute for X, while good Z are complement for X.

(b). Is X an inferior or a normal good?

X is a normal good.

(c). How many units of good X will be purchased when Px= $4,910??

Q = 1,200 – $4,910/2 + $5,900/4 – 8 x $90 + $55,000/10 = 5000 units

(d). Determine the demand function and inverse demand function for good X. Graph the demand curve for good X.

Q = 1200 – 0.5 Px = 1475 - 720+ 5,500 = 7455 – ½ Px

½ Px = 7466-QxPx = 14,910-2Qx

Price

14,910

7455

Question 3(Refer to question 2 of page 66 from ME textbook)

• Good X is produced in a competitive market using input A. Explain what would happen to the supply of good X in each of the following situations:A) The price of input A increasesB) An excise tax of $1 is imposed on good XC) An ad valorem tax of 5% is imposed on good XD) A technological change reduces the cost of producing

additional units of good X.

Question 3(Refer to question 2 of page 66 from me textbook)

A) The price of input A increases

Price

Quantity of Good X

S0

S1

Cost of producing good X increases

Supplier is less willing to produce more.

Therefore, supply of good X will decrease.

Supply curve of good X will shift to the left.

Question 3(Refer to question 2 of page 66 from me textbook)

B) An excise tax of $1 is imposed on good X

Supplier is willing to supply the same quantity of good X when he receives additional $1 per unit of good X.

Price

Quantity of Good X

S0

S0 + t

$1

Selling price per unit + $1 excise tax.

Supply curve will shift vertically up by exactly $1 for each output level.

Question 3(Refer to question 2 of page 66 from me textbook)

C) An ad valorem tax of 5% is imposed on good X

Supplier is willing to supply

the same quantity of good X when the unit price of production goes up by 5%.

Price

Quantity of Good X

S0

S0 x 1.05 t

Selling price per unit x 5% ad valorem tax.

Supply curve will rotate counterclockwise. The new curve will shift farther away from original curve when the price increases.

Question 3(Refer to question 2 of page 66 from me textbook)

D) A technological change reduces the cost of producing additional units of good X

Supplier is willing to produce more.

Price

Quantity of Good X

S0

S1

Supply of good X will increase.

Supply curve will shift to the right.

QUESTION 4(Refer to question 7 of page 67 from me textbook)

• Suppose demand and supply are given by

QDX = 7 – ½ PX and QS

X = ¼ PX – ½

A) Determine the equilibrium price and quantity. Show the equilibrium graphically.

B) Suppose a $6 excise tax is imposed on the good. Determine the new equilibrium price and quantity.

C) How much tax revenue does the government earn with the $6 tax?

QUESTION 4(Refer to question 7 of page 67 from me textbook)

Market equilibrium occurs when market supply intersects with market demand

QDX = QS

X

7 – ½ PX = ¼ PX – ½

¾ PX = 7 ½

PX = $10

Determine the equilibrium price and quantity. Show the equilibrium graphically.

QUESTION 4(Refer to question 7 of page 67 from me textbook)

Using demand equation:

QDX = 7 – ½ PX

QDX = 7 – ½ (10)

QDX = 7 – 5

QDX = 2 units

Equilibrium price = $10Equilibrium quantity = 2 units

Question 4(Refer to question 2 of page 67 from me textbook)

Price

Quantity of Good X1 2 3 4 5 6 7

2

4

6

8

10

12

14

16

18

20

0

Supply

Demand

PX = 2 + 4Qs

Equilibrium

QUESTION 4(Refer to question 7 of page 67 from me textbook)

B) Suppose a $6 excise tax is imposed on the good. Determine the new equilibrium price and quantity.

Price

Quantity of Good X

1 2 3 4 5 6 7

2

4

6

8

10

12

14

16

18

20

0

So PX = 2 + 4Qs

So + t PX = 8 + 4Qs

Supply equation without tax:PX = 2 + 4QS

Supply equation with tax:PX = 2 + 4QS + 6PX = 8 + 4QS

So, QS = ¼ PX - 2

QUESTION 4(Refer to question 7 of page 67 from me textbook)

• To calculate new equilibrium price and quantity:QD

X = 7 – ½ PX

QSX = ¼ PX – 2

7 – ½ PX = ¼ PX – 2

¾ PX = 7 + 2

PX = $12

QDX = 7 – ½ (12)

QDX = 1 unit

New equilibrium price = $12New equilibrium quantity = 1 unit

QUESTION 4(Refer to question 7 of page 67 from me textbook)

C) How much tax revenue does the government earn with the $6 tax?

Unit sold after tax = 1Tax

= $6Therefore, Tax revenue =

1 x $6 Tax revenue =

$6