- 25 Marks
Question
The demand and supply functions are given below:
a) P = 900 – 0.5Q and P = 300 + 0.25Q. What is the equilibrium price and quantity? (10 marks)
The table below shows the quantity of products supplied and demanded per week in Kaneshie market.
| Quantity Demanded | Quantity Supplied | Price |
|---|---|---|
| 8 | 57 | 10 |
| 10 | 35 | 8 |
| 15 | 30 | 6 |
| 18 | 28 | 5 |
| 25 | 25 | 4 |
| 26 | 22 | 3 |
| 30 | 18 | 3 |
| 32 | 15 | 2 |
| 35 | 10 | 1 |
b) Graphically determine the equilibrium point, explaining the circumstances under which there will be excess demand and supply. (15 marks)
Answer
a) Set demand equal to supply: 900 – 0.5Q = 300 + 0.25Q.
Add 0.5Q to both sides: 900 = 300 + 0.75Q.
Subtract 300: 600 = 0.75Q.
Q = 600 / 0.75 = 800.
P = 300 + 0.25 × 800 = 300 + 200 = 500 (or 900 – 0.5 × 800 = 900 – 400 = 500).
Equilibrium: Price 500, Quantity 800.
In banking, this models loan supply/demand, where equilibrium interest rates balance under BoG guidelines.
b) Plot Quantity on x-axis, Price on y-axis. Demand curve: Connect points from table (e.g., at P=10, Qd=8; P=8, Qd=10, etc., downward sloping). Supply curve: (P=10, Qs=57; P=8, Qs=35, etc., upward sloping, note duplicate P=3 for Qs=22 and 18, perhaps average or plot separately).
Equilibrium where curves intersect: From table, at P=4, Qd=25, Qs=25, so equilibrium Price 4, Quantity 25.
Excess demand (shortage): When Qd > Qs, below equilibrium price (e.g., at P=3, Qd=26 or 30 > Qs=22 or 18), prices rise.
Excess supply (surplus): When Qs > Qd, above equilibrium (e.g., at P=6, Qs=30 > Qd=15), prices fall.
In Ghana’s markets like Kaneshie, this applies to forex or commodity trading, influencing bank strategies under volatile exchange rates.
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