Final answer:
Using Jin's demand function and the price of Good X, we calculate his consumer surplus as the area of a triangle below his maximum willingness to pay and above the market price. The calculated consumer surplus comes out to be $150 when the price of Good X is $15 per unit, making the answer D. $150.
Step-by-step explanation:
To calculate the value of Jin's consumer surplus for Good X, when the price is $15 per unit, we use his demand function q = 15 - P/3. First, we find the quantity demanded at the price of $15. Substituting P = $15 into the demand function, we get:
q = 15 - 15/3
q = 15 - 5
q = 10 units
Next, we identify the maximum price Jin is willing to pay for the last unit he purchases (the 10th unit), by setting q = 0:
0 = 15 - P/3
P = 15 × 3
P = $45
So, Jin would be willing to pay $45 for the first unit of Good X. Consumer surplus is the area below this maximum price and above the market price, up to the quantity that Jin purchases.
The consumer surplus is thus calculated as the area of the triangle formed by the maximum price Jin is willing to pay for the first unit, the quantity he buys, and the market price. The formula for the area of a triangle is 1/2 base × height:
Consumer Surplus = 1/2 × (45 - 15) × 10
Consumer Surplus = 1/2 × 30 × 10
Consumer Surplus = $150
Jin's consumer surplus when the price of Good X is $15 per unit is therefore $150. So the answer is D. $150.