- 20 Marks
Question
Cocoa and Coffee are common cash crops in Ghana. The knowledge of their Demand and Supply is crucial for national development. Assume the Demand and Supply functions of Cocoa are given as $Q^d=12-p$ and $Q^s=9.6+0.5 p-0.2 p_c$ respectively. Where $Q^d$ is Quantity Demanded and $Q^s$ is Quantity Supplied of Cocoa, $p$ is the Price of Cocoa and $p_c$ is the Price of Coffee. (a) Determine the Equilibrium Price and Quantity of Cocoa if $p_c=\mathrm{GHC} 3.00$. [6 marks]
(b) Determine the new Equilibrium Price and Quantity of Cocoa if the price of Coffee increases from its original price of $p_c=\mathrm{GHC} 3.00$ to $\mathrm{GHC} 6.00$. [6 marks]
(c) Represent the solutions in $a$ and $b$ above with a diagram. [6 marks]
(d) Explain whether Cocoa and Coffee have Joint, Composite or Competitive Supply.[2 marks]
(Total: 20 marks)
Answer
(a) At equilibrium, Q^d = Q^s.
Substitute p_c = 3: Q^s = 9.6 + 0.5p – 0.2(3) = 9.6 + 0.5p – 0.6 = 9 + 0.5p.
Set 12 – p = 9 + 0.5p.
12 – 9 = p + 0.5p → 3 = 1.5p → p = 2 GHC.
Quantity: Q = 12 – 2 = 10 units.
To solve: Add p to both sides: 12 = 9 + 1.5p → 3 = 1.5p → p=2. Yes.
(b) New p_c = 6: Q^s = 9.6 + 0.5p – 0.2(6) = 9.6 + 0.5p – 1.2 = 8.4 + 0.5p.
Set 12 – p = 8.4 + 0.5p.
12 – 8.4 = p + 0.5p → 3.6 = 1.5p → p = 2.4 GHC.
Quantity: Q = 12 – 2.4 = 9.6 units.
The increase in coffee price shifts cocoa supply leftward (negative coefficient -0.2p_c indicates competitive supply), raising equilibrium price and lowering quantity.
(c) Diagram representation (textual description, as image generation requires confirmation):
- Original: Demand curve: downward sloping from (p=0, Q=12) to (p=12, Q=0).
Supply original: upward sloping, intercept 9 at p=0, slope 0.5.
Equilibrium at (p=2, Q=10).
- New supply: shifts left, intercept 8.4 at p=0.
New equilibrium at (p=2.4, Q=9.6).
Sketch: Demand line, two supply lines (S1 original, S2 new leftward), intersections E1 and E2.
(d) Cocoa and coffee have competitive supply, as they compete for shared resources like land and labor in Ghana. The negative coefficient (-0.2p_c) in the supply function shows that higher coffee prices reduce cocoa supply, indicating substitution in production rather than joint (simultaneous output) or composite (combined use) supply.
- Topic: Price and Output - The Commodity/Industry and the Market
- Series: APR 2024
- Uploader: Samuel Duah