In a competitive market the demand and supply curves are as follows:Demand: Qd = 143 – 2PSupply: Qs = P/2 - 8.What is the total surplus (TS) in the competitive market equilibrium? [Round your answer to 1 decimal place (e.g. 24.3)]
Question
In a competitive market the demand and supply curves are as follows:Demand: Qd = 143 – 2PSupply: Qs = P/2 - 8.What is the total surplus (TS) in the competitive market equilibrium? [Round your answer to 1 decimal place (e.g. 24.3)]
Solution
To find the total surplus in the competitive market equilibrium, we first need to find the equilibrium price and quantity. This is where the quantity demanded (Qd) equals the quantity supplied (Qs).
Setting Qd equal to Qs, we have:
143 - 2P = P/2 - 8
Solving for P, we get:
P = 50
Substituting P = 50 into either the demand or supply equation, we can find the equilibrium quantity. Let's use the demand equation:
Q = 143 - 2*50 = 43
The total surplus is the sum of the consumer surplus and the producer surplus. The consumer surplus is the area between the demand curve and the price line up to the equilibrium quantity, and the producer surplus is the area between the price line and the supply curve up to the equilibrium quantity.
The consumer surplus is given by the area of a triangle with base 43 and height (143 - 50) = 93, so:
Consumer Surplus = 0.5 * 43 * 93 = 1999.5
The producer surplus is given by the area of a triangle with base 43 and height (50 - (-8)) = 58, so:
Producer Surplus = 0.5 * 43 * 58 = 1247
Therefore, the total surplus is:
Total Surplus = Consumer Surplus + Producer Surplus = 1999.5 + 1247 = 3246.5
So, the total surplus in the competitive market equilibrium is 3246.5. Rounded to one decimal place, this is 3246.5.
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