The linear demand curve is represented by the equation
A) $P = Q - a P$
B) $Q = a - b P$
C) $Q = a - b P ^ { 2 }$
D) $Q = A P - b$

Question

The linear demand curve is represented by the equation 
A) $P = Q - a P$
B) $Q = a - b P$
C) $Q = a - b P ^ { 2 }$
D) $Q = A P - b$

Quizplus · Accepted Answer

The linear demand curve can be written as Q = a - bP, where a is the quantity demanded when P equals zero and b is the slope of the curve. This equation shows an inverse relationship between P and Q, which is a characteristic of a demand curve. Choices A and C both include a negative P coefficient, which suggests that an increase in price would lead to a decrease in quantity demanded - however, the squared term in choice C indicates a non-linear relationship. Choice D includes a positive coefficient for P, which is inconsistent with a demand curve. Therefore, the correct choice is B. The linear demand curve is represented by a straight line that shows the relationship between price and quantity demanded. The equation that represents this relationship should be in the form of Q = a - bP, where Q represents quantity demanded, P represents price, and a and b are constants. This equation shows a negative relationship between price and quantity demanded, which is the characteristic of a linear demand curve. The other options either include a quadratic term or a constant that is not multiplied by P, which would result in a non-linear demand curve.

The Linear Demand Curve Is Represented by the Equation P=Q−aPP = Q - a PP=Q−aP

The Linear Demand Curve Is Represented by the Equation $P = Q - a P$