1. Market demand is given as QD = 250 – 0.5P. Market supply is given as QS = 2P. In a perfectly competitive equilibrium, what will be the value of consumer surplus?
a.$10 000
b.$20 000
c.$40 000
d.$80 000
2. Market demand is given as QD = 250 – 0.5P. Market supply is given as QS = 2P. In a perfectly competitive equilibrium, what will be the value of producer surplus?
a.$10 000
b.$20 000
c.$40 000
d.$80 000
1.A
2.b
To find the value of consumer surplus and producer surplus in a perfectly competitive equilibrium, we need to find the equilibrium price and quantity. We can do this by setting the quantity demanded and quantity supplied equal to each other.
1. Market demand: QD = 250 - 0.5P
Market supply: QS = 2P
Setting QD equal to QS:
250 - 0.5P = 2P
Combining like terms:
250 = 2.5P
Dividing both sides by 2.5:
P = 100
Now, substitute the equilibrium price (P = 100) into either the demand or supply equation to find the equilibrium quantity:
QD = 250 - 0.5P
QD = 250 - 0.5(100)
QD = 250 - 50
QD = 200
So, in a perfectly competitive equilibrium, the price is $100 and the quantity is 200.
To calculate consumer surplus, we need to find the area between the demand curve and the equilibrium price line. The formula for consumer surplus is:
Consumer Surplus = 0.5(QD) * (Price without Surplus)
Consumer Surplus = 0.5(200) * (250 - 100)
Consumer Surplus = 0.5(200) * 150
Consumer Surplus = 100 * 150
Consumer Surplus = 15,000
Therefore, the value of consumer surplus is $15,000.
To calculate producer surplus, we need to find the area between the supply curve and the equilibrium price line. The formula for producer surplus is:
Producer Surplus = 0.5(QS) * (Price without Surplus)
Producer Surplus = 0.5(200) * (100 - 0)
Producer Surplus = 0.5(200) * 100
Producer Surplus = 100 * 100
Producer Surplus = 10,000
Therefore, the value of producer surplus is $10,000.
So, the correct answer for question 1 is: a. $10,000.
And the correct answer for question 2 is: a. $10,000.
To determine the value of consumer surplus and producer surplus in a perfectly competitive equilibrium, we first need to find the equilibrium price and quantity.
1. To find the equilibrium price, we set the quantity demanded (QD) equal to the quantity supplied (QS):
QD = QS
250 - 0.5P = 2P
Simplifying the equation:
250 = 2.5P
Divide both sides by 2.5:
P = 100
2. Substituting the equilibrium price (P = 100) into either the demand or supply equation, we can find the equilibrium quantity:
QD = 250 - 0.5P
QD = 250 - 0.5(100)
QD = 250 - 50
QD = 200
3. Now that we have the equilibrium price (P = 100) and quantity (Q = 200), we can calculate consumer surplus.
Consumer surplus is the difference between the price consumers are willing to pay (their valuations) and the price they actually pay.
To calculate the consumer surplus, we need the demand function QD = 250 - 0.5P.
Substituting the equilibrium price (P = 100) into the demand function:
QD = 250 - 0.5(100)
QD = 250 - 50
QD = 200
Now we can calculate consumer surplus:
Consumer surplus = ∫(Pmax - P) dQ
Consumer surplus = ∫(100 - P) dQ (from Q = 0 to Q = 200)
Consumer surplus = ∫(100 - (250 - 0.5P)) dQ
Consumer surplus = ∫(100 - 250 + 0.5P) dQ
Consumer surplus = ∫(0.5P - 150) dQ
Consumer surplus = 0.5∫P dQ - 150∫dQ
Consumer surplus = 0.5[PQ] - 150[Q]
Substituting the values Q = 200 and P = 100 into the equation:
Consumer surplus = 0.5(100)(200) - 150(200)
Consumer surplus = 10,000 - 30,000
Consumer surplus = -20,000
Since the calculated consumer surplus is negative, none of the provided answer choices (a, b, c, d) are correct.