The demand and supply function of a commodity are given as follows: Quantity demanded (Qd) = 20 - 2p Quantity supplied (Qs) = 6P - 12 where P = price in nai...

Answer Details

(a) Equilibrium price and quantity. Equilibrium occurs where quantity demanded equals quantity supplied, \(Q_d = Q_s\):

\[ 20 - 2P = 6P - 12 \]

\[ 20 + 12 = 6P + 2P \;\Rightarrow\; 32 = 8P \;\Rightarrow\; P = 4 \]

Substituting \(P = 4\) into either function: \(Q_d = 20 - 2(4) = 12\). So the equilibrium price is N4.00 and the quantity bought and sold is 12 units.

(b) Excess supply at the fixed price. At a price above equilibrium, quantity supplied exceeds quantity demanded, giving excess supply (a surplus). Excess supply \(= Q_s - Q_d\). Taking the fixed price as N6.00 (the sensible value above the equilibrium of N4):

\[ Q_s = 6(6) - 12 = 24, \qquad Q_d = 20 - 2(6) = 8 \]

\[ \text{Excess supply} = 24 - 8 = 16 \text{ units} \]

The magnitude of the excess supply is therefore 16 units. (Note: the figure printed as N60.00 is almost certainly a typographical error for N6.00, since a price of N60 lies far outside the range of these functions.)