Question

1. The demand for good x is given as Qd:

Qd = 1000 – 5Px – 0.5I – 10Py + 2Pz – 3Pc

Where, Qd = quantity demanded of good x (in thousand units)

    Px = price of good x

    I = consumer incomes (in thousand)

    Py = price of good y

    Pz = price of good z

    Pc = price of good c

1. If consumer incomes are 30 (in thousand), price of good y is 15, price of good z is 25, and price of good c is 35, what is the demand curve for good x?

2. What is the quantity demanded of good x by consumers if the price of good x is 15?

3. Suppose the price of good c decreases to 30 from 35. What is the new demand curve for good x?

4. What is the new quantity demanded of good x, if the price of good x remains the same at 15 based on the new demand curve?

5. What is the effect of a decrease in price of good c on the demand for good x? What is the relationship of good c and good x? Why?  

Answer 1

We are given the demand for good x as :

Qd = 1000 – 5Px – 0.5I – 10Py + 2Pz – 3Pc

Where, Qd = quantity demanded of good x (in thousand units)

    Px = price of good x

    I = consumer incomes (in thousand)

    Py = price of good y

    Pz = price of good z

    Pc = price of good c

a) When I = 30 , Py = 15 , Pz = 25 and Pc = 35 ; The demand curve of good x can be derived as:

Qd = 1000 - 5Px - 0.5(30) – 10(15) + 2(25) – 3(35)

Qd = 1000 - 5Px - 15 – 150 + 50 – 105

Qd = 780 – 5Px

b) If the price of good x is Px = 15, then the quantity demanded for good x will be :

Qd = 780 – 5Px

Qd = 780 – 5(15)

Qd = 780 – 75

Qd = 705 (in thousand)

c) If price of good c decrease from 35 to 30, the new demand curve for good x will be:

Qd = 1000 – 5Px – 0.5I – 10Py +2Pz - 3Pc

Qd = 1000 – 5Px – 0.5(30) – 10(15) + 2(25) – 3(30)

Qd = 1000 – 5Px –15 – 150 + 50 – 90

Qd = 795 – 5Px

d)The new quantity demanded for good x, when Px = 15 will be:

Qd = 795 – 5Px

Qd = 795 – 5(15)

Qd = 795 – 75

Qd = 720 (in thousand)

e) As we can see when the price of good c fell from 35 to30, the quantity demanded for good X increases from 705000 to 720000. This means there is an inverse relationship between the demand of good x and the price of good c. This makes both the goods as complementary goods in relation. Complementary goods are those goods where in if price of good one falls the demand for other goods increases and if price of one good rise then the demand of other good falls.