Assume that a certain commodity's demand equation has the form p = ax + b, where x is the quantity demanded and p is the unit price in dollars. Suppose the quantity demanded is 1,000 units when the unit price is $19.00 and 7,000 when the unit price is $13.00. What is the quantity demanded when the unit price is $18.50?
A) 6,000 units
B) 1,500 units
C) 6,500 units
D) 8,000 units

Question

Quizplus · Accepted Answer

To find the demand equation, use the two points (1000, 19) and (7000, 13) to find the slope (a) and intercept (b). The slope a = (13 - 19) / (7000 - 1000) = -1/1000. Using point (1000, 19), solve for b: 19 = (-1/1000)(1000) + b, so b = 20. The equation is p = -1/1000 * x + 20. For p = 18.50, solve 18.50 = -1/1000 * x + 20, giving x = 1500.

Assume That a Certain Commodity's Demand Equation Has the Form