Question

Imagine the market for Good X has a demand function of Qdx = 200 – 2Px – Py + .1M and a supply function of Qsx = 2Px – 2Pw, where Px is the price of Good X, Py is the price of Good Y, and M is the average consumer income. Pw is the price of Good W, which is an input to the production of Good X.

If Py = 10, Pw = 50, M = $2700, what's the price of X in equilibrium?

Answer 1

At the equilibrium, $Q_{dx}=Q_{sx}$:

$$200-2P_x-P_y+0.1M=2P_x-2P_w,$$ $$200-2P_x-\$10+0.1\cdot\$2700=2P_x-2\cdot\$50,$$ $$4P_x=\$560,$$ $$P_x=\$140.$$