객관식
The supply and demand curves for a product are as follows. What is consumer surplus in this market?
QD = 45 – 2P
QS = -15 + P
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5. Consumer and Producer Surplus; Price Ceilings and Price Floors
Quantitative Analysis of Consumer and Producer Surplus at Equilibrium
객관식
How do you calculate consumer and producer surplus at equilibrium?
A
Find equilibrium P* and Q*; CS = (maximum willingness-to-pay − P*) × Q*; PS = (P* − supply intercept) × Q*
B
Find equilibrium P* and Q*; CS = ∫_0^{Q*} (P* − P_d(Q)) dQ; PS = ∫_0^{Q*} (P_s(Q) − P*) dQ
C
Find equilibrium P* and Q*; CS = 1/2 × (maximum willingness-to-pay − P*) × Q*; PS = 1/2 × (P* − supply intercept) × Q*
D
Find equilibrium P* and Q*; CS = 1/2 × (P* − maximum willingness-to-pay) × Q*; PS = 1/2 × (supply intercept − P*) × Q*
검증된 단계별 안내1
First, find the equilibrium price (P*) and quantity (Q*) by setting the demand function equal to the supply function and solving for P and Q. This means solving the equation: \[\text{Demand}(Q) = \text{Supply}(Q)\] to find the values of P* and Q* where quantity demanded equals quantity supplied.
Next, identify the maximum willingness-to-pay, which is the price intercept of the demand curve (the price at which quantity demanded would be zero). This represents the highest price consumers are willing to pay for the first unit.
Calculate the consumer surplus (CS) as the area between the demand curve and the equilibrium price, up to the equilibrium quantity. Since the demand curve is typically linear, this area forms a triangle. Use the formula for the area of a triangle: \[CS = \frac{1}{2} \times (\text{maximum willingness-to-pay} - P^*) \times Q^*\].
Identify the supply intercept, which is the price at which quantity supplied would be zero. This is the lowest price producers are willing to accept to supply the first unit.
Calculate the producer surplus (PS) as the area between the supply curve and the equilibrium price, up to the equilibrium quantity. This area is also a triangle, so use the formula: \[PS = \frac{1}{2} \times (P^* - \text{supply intercept}) \times Q^*\].
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