Question

Assume that demand for a commodity is represented by the equation P = 10 - 0.2Q and supply by the equation P = 2 + 0.2Q. Find equilibrium price and quantity (algebraically). Then graph the supply and demand lines, plot equilibrium point and label axes, equilibrium P* and Q*, vertical and horizontal intercepts for demand curve, and vertical intercept for the supply curve.

Answer 1

In equilibrium, Demand price equals supply price.

10 - 0.2Q = 2 + 0.2Q

0.4Q = 8

Q = 20

P = 10 - (0.2 x 20) = 10 - 4 = 6

From demand function,

When Q = 0, P = 10 (Vertical intercept) & When P = 0, Q = 10/0.2 = 50 (Horizontal intercept)

From supply function,

When Q = 0, P = 2 (Vertical intercept)

In following graph, Price (P) & Quantity (Q) are measured vertically & horizontally. AB & CD are demand & supply curves intersecting at point E with price P* (= 6) and quantity Q* (= 20).