Final answer:
To find the consumer surplus, we need to calculate the area between the demand curve and the equilibrium price. The consumer surplus at the equilibrium price of $20 is $0.
Step-by-step explanation:
To find the consumer surplus, we need to calculate the area between the demand curve and the equilibrium price.
The consumer's demand curve for the good is given as P=50−5Qd, where P is the price and Qd is the quantity demanded. The equilibrium price is $20.
Substitute the equilibrium price into the demand curve equation to find the equilibrium quantity: 20 = 50 - 5Qd. Solve for Qd: Qd = 6.
To find the consumer surplus, we need to calculate the area between the equilibrium price and the demand curve, from Q=0 to Q=6.
The formula for the consumer surplus is 0.5 * (Qd) * (Pmax - Pmin), where Qd is the equilibrium quantity, Pmax is the maximum price consumers are willing to pay, and Pmin is the equilibrium price.
In this case, Qd = 6, Pmax = 50 - 5 * 6 = 20, and Pmin = 20.
Substitute the values into the formula: Consumer Surplus = 0.5 * 6 * (20 - 20) = 0.
Therefore, the consumer surplus at the equilibrium price of $20 is $0.
The consumer surplus is found using the area of a triangle, with the base being the equilibrium quantity demanded and the height being the difference between the maximum price willing to be paid and the equilibrium price. However, the calculated consumer surplus of 90 doesn't match any of the provided options, suggesting an error in the options or the data given.
The question at hand involves calculating the consumer surplus at the equilibrium price given a consumer's demand curve for a good represented by the equation P=50−5Qd, where P is the price and Qd is the quantity demanded. To find the consumer surplus, we need to consider the area above the equilibrium price and below the demand curve. The equilibrium price given is $20, so by substituting this value into the demand equation we find the quantity demanded at equilibrium (Qd):
20 = 50 − 5Qd → 5Qd = 30 → Qd = 6.
The consumer surplus is the area of the triangle that forms between the y-axis, the demand curve, and a horizontal line at the equilibrium price. The formula for the area of a triangle is (base × height) / 2. In this context, the base is the quantity demanded at equilibrium, and the height is the difference between the maximum price consumers are willing to pay (as per the demand curve when quantity is zero, which is $50) and the equilibrium price ($20), yielding:
Consumer Surplus = (6 × (50 - 20)) / 2 = (6 × 30) / 2 = 180 / 2 = 90.
However, none of the given options (A. 280 B. 100 C. 120 D. 240) matches this calculated consumer surplus. There may be an error in the provided options or the calculation, and it would be appropriate to double-check both the demand curve equation and the options provided. If there is no error in the data provided, the correct approach would be to communicate the discrepancy to the student and explain the method to calculate consumer surplus correctly.