The demand curve is 𝐷 =16 − 3𝑝 and the supply curve is 𝑆 = −4 + 2𝑝.(a) [5 marks]Find the competitive equilibrium.(b) [10 marks]Compute the consumer surplus and producer surplus.
Question
The demand curve is 𝐷 =16 − 3𝑝 and the supply curve is 𝑆 = −4 + 2𝑝.(a) [5 marks]Find the competitive equilibrium.(b) [10 marks]Compute the consumer surplus and producer surplus.
Solution
(a) To find the competitive equilibrium, we need to set the demand equal to the supply and solve for the price (p) and quantity (D or S).
16 - 3p = -4 + 2p
Combine like terms:
5p = 20
Solve for p:
p = 20 / 5 = 4
Substitute p = 4 into either the demand or supply equation to find the equilibrium quantity. Let's use the demand equation:
D = 16 - 3(4) = 16 - 12 = 4
So, the competitive equilibrium is at price p = 4 and quantity Q = 4.
(b) Consumer surplus is the area between the demand curve and the price level up to the quantity sold. It's calculated as:
Consumer Surplus = 0.5 * (Maximum price consumers are willing to pay - Actual price) * Quantity
Maximum price consumers are willing to pay can be found when price (p) is 0 in the demand equation:
D = 16 - 3(0) = 16
So, Consumer Surplus = 0.5 * (16 - 4) * 4 = 24
Producer surplus is the area between the supply curve and the price level up to the quantity sold. It's calculated as:
Producer Surplus = 0.5 * (Actual price - Minimum price suppliers are willing to accept) * Quantity
Minimum price suppliers are willing to accept can be found when supply (S) is 0 in the supply equation:
0 = -4 + 2p
Solve for p:
p = 4 / 2 = 2
So, Producer Surplus = 0.5 * (4 - 2) * 4 = 4
Therefore, the consumer surplus is 24 and the producer surplus is 4.
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