Final answer:
The price elasticity of demand for the given function Q = 100 - 4p is calculated as -2/3 at the initial price, indicating that the demand is inelastic when the price decreases from $10 to $8.
Step-by-step explanation:
The student's question relates to the point price elasticity of demand when the price of a good decreases from $10 to $8. Given the demand function Q = 100 - 4p, where 'Q' is quantity demanded and 'p' is the price of the good, we can calculate elasticity using the formula of elasticity E = (p/Q) * (dQ/dp).
To find the derivative of Q with respect to p, we differentiate the demand function to get dQ/dp = -4. Now, substituting the initial price and quantity (before the price change) into the formula, we have E = (10 / (100 - 4*10)) * (-4). This simplifies to E = (10 / 60) * (-4) = -2/3, which means the demand is inelastic at that point. As the price decreases, the quantity demanded increases, but not enough to offset the decrease in price, resulting in lower total revenue.