Final answer:
By calculating the change in quantity demanded from a 1% increase in the price of the own good from the given demand equation, we find that the own price elasticity of demand is -0.505. This indicates that demand is relatively inelastic, as the absolute value is less than one. The correct answer to the question is (d) -0.50; relatively inelastic.
Step-by-step explanation:
The student has provided the following equation for demand: Qx = 50 - 10 (Px) + 4 (Py) + 8 (Inc), where Px is the price of the own good, Py is the price of a related good, and Inc is the income of buyers. The given values are Px = $10, Py = $12, and Inc = $25,000 (for calculations, use 25). To calculate the own price elasticity, we'll need to find the percentage change in quantity demanded resulting from a one percent change in the price of the own good (Px).
The initial quantity demanded (Qx0) is calculated by substituting the given prices and income into the demand equation:
Qx0 = 50 - 10(10) + 4(12) + 8(25) = 50 - 100 + 48 + 200 = 198
Next, we increase Px by 1% (from $10 to $10.10) and calculate the new quantity demanded (Qx1):
Qx1 = 50 - 10(10.10) + 4(12) + 8(25) = 50 - 101 + 48 + 200 = 197
The percentage change in quantity demanded is then:
Percentage change in quantity demanded = [(197 - 198) / 198] × 100 = -0.505%
The own price elasticity of demand is the percentage change in quantity demanded divided by the percentage change in price, which equals -0.505% / 1% = -0.505, implying that the demand is relatively inelastic as the absolute value of the elasticity is less than 1.
Therefore, the correct answer from the options provided is (d): -0.50; relatively inelastic.