In the equation Q = a - bp + e; Q and P are ... Variables respectively.

Analyze the question The equation Q = a - bp + e is a simple demand function (a regression-style equation). We are asked what kind of variables Q and P are.

Explain the concept

• In a demand equation, quantity demanded (Q) depends on price (P). So Q is the dependent variable, because its value is determined by the other terms.
• Price (P) is the independent variable, because it is the input that changes Q.
• a is the intercept (a constant), b is the slope coefficient (the effect of price on quantity), and e is the error (stochastic) term.

Step-by-step solution

1. Identify the variable on the left-hand side: Q. It is the outcome being explained, so it is dependent.
2. Identify the variable on the right-hand side that is being varied: P. It explains Q, so it is independent.
3. Check the options: • A. independent and dependent: this reverses the roles. ✗ • B. dependent and independent: Q is dependent and P is independent. ✓ • C. independent and constant: P is not a constant. ✗ • D. error term and independent: Q is not the error term, since e is the error term. ✗

Answer: Q is the dependent variable and P is the independent variable, which is option B.

Exam tip In any equation of the form Y = a + bX + e, remember "Y depends on X". The variable on the left is dependent, and the one multiplied by a coefficient is independent. The letter "a" is the constant, "b" is the coefficient, and "e" is the error term.