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 z decreases to 20. 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 z on the demand for good x? What is the relationship of good z and good x? Why?

Please show solutions and formulas used

Answer 1

Ans: Q_d = 1000 - 5P_x - 0.5l - 10P_y + 2P_z - 3P_c

(a) Given the values of l = 30 (in thousand) P_y = 15; P_z =25; P_c = 35

putting the values in the Q_d we get:

Q_d = 1000 - 5P_x - 0.5 × 30 - 10 × 15 + 2 × 25 - 3 × 35

Q_d = 1000 - 5P_x - 15 - 150 + 50 - 105

Q_d = 1000 - 5P_x - 165 + 50 - 105

Q_d = 1000 - 115 - 105 - 5P_x

Q_d = 780 - 5P_x

This is the demand curve for good x.

(b) If the price of good x is 15. P_x = 15

Quantity demanded for good X is

Q_d = 780 - 5P_x

Q_d = 780 - 5 × 15

Q_d = 705

Thus demand for good x = 705

(c) If the price for good z decreases to 20 now P_z = 20

Then new demand curve is:

Q_d = 1000 - 5P_x - 0.5l - 10P_y + 2P_z - 3P_c

Q_d = 1000 - 5P_x - 0.5 × 30 - 10 × 15 + 2 × 20 - 3 × 35

Q_d = 1000 - 5P_x - 15 - 150 + 40 - 105

Q_d = 1000 - 5P_x - 165 + 40 - 105

Q_d = 1000 - 230 - 5P_x

Q_d = 770 - 5P_x

This is the new demand curve for x

(d) If the price of good x is 15. P_x = 15

Putting the value of P_x in the new demand curve we get:

Q_d = 770 - 5P_x

Q_d = 770 - 5 × 15

Q_d = 770 - 75 = 695

Thus new quantity demanded for good x = 695

(e) When the price of good z decreases from 25 to 20 then the quantity demanded of good x decreases from 705 to 695; thus there is negative realtionship between the price of good z and the quantity demanded of good x

This implies that goods x and z are complementary goods which implies both good x and z complement each other which implies that price of one good is negatively related to the demand of other good.