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.
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).
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