Question

Assume that the demand for product X is represented by the following equation: Qdx = 1000-10Px +2Py – 4Pz

i) Which of the products Y and Z is a substitute to X in consumption? Which is a complement? Explain.

ii) If you are told that Py = 25 and Pz = 50, find the simple linear demand equation and graph it.

Answer 1

Qdx = 1000-10Px +2Py – 4Pz

(1) The coefficient of variable Py is positive. It implies that there is positive relationship between quantity demand of good X and price of good y. A rise in the price of good y leads to rise in the demand for good X. Hence, Good X and Good Y are substitute goods.

The coefficient of variable Pz is negative. It implies that there is negative relationship between quantity demand of good X and price of good z. A rise in the price of good z leads to fall in the demand for good X. Hence, Good X and Good Z are complement goods.

(2)  Qdx = 1000-10Px +2Py – 4Pz

Put Py = 25 and Pz = 50

Qdx = 1000-10Px +2(25) – 4(50)

Qdx = 1000-10Px +50 - 200

Qdx = 850-10Px (Simple linear demand equation)

90 80 70 60 50 40 30 20 10 100 200 300 400 500 600 700 800 900 Qdx

Note: For Y axis intercept, put Qdx = 0 in simple linear demand equation and solve for Px

For X axis intercept, put Px = 0 in simple linear demand equation and solve for Qdx.