Question

Given a linear demand function of the form Qdx=500 -2Px-3Py+0.01M, find the inverse linear demand function assuming M=20,000 and Py=10. Graph the demand curve.

Answer 1

Required function would be the relationship between quantity demanded (Qdx) and the price of x (Px).

Given, Qdx = 500 – 2Px – 3Py + 0.01M

Again given, M = 20,000 and Py = 10

Therefore, Qdx = 500 – 2Px – 3Py + 0.01M

Qdx = 500 – 2Px – (2 × 10) + (0.01 × 20,000)

        = 500 – 2Px – 20 + 200

        = 680 – 2Px

Let Qdx is Q and Px is P

Q = 680 – 2P

The inverse function should be arranged as below:

680 – 2P = Q

2P = 680 – Q

P = 340 – 0.5Q [Answer]

Graph is as below:

If (Q = 0), P = 340 – 0, P = 340; therefore, coordinates (Q, P) is (0, 340).

If (P = 0), 0 = 340 – 0.5Q, 0.5Q = 340, Q = 680; therefore, coordinates (Q, P) is (680, 0).

These coordinates are pointed in a graph to draw the following demand curve.

340 13 680 The demand curve is D