Microeconomics Diagnostic Quiz – Step-by-Step Guidance

Q4. Graphing a Linear Demand Function

Background

Topic: Demand Functions and Graphing

This question tests your understanding of how to graph a linear demand function, identify intercepts, and calculate the slope. These are foundational skills in microeconomics for analyzing market demand.

Key Terms and Formulas

• Demand Function: A mathematical relationship showing how quantity demanded (Q) depends on price (P).

• Intercepts: The points where the graph crosses the axes (Q-intercept and P-intercept).

• Slope: The rate at which P changes as Q changes. For a linear function $P = a + bQ$, the slope is $b$.

Step-by-Step Guidance

1. Start with the given demand function: $P = 60 - 3Q$.

2. To find the P-intercept (where $Q = 0$), substitute $Q = 0$ into the equation and solve for $P$.

3. To find the Q-intercept (where $P = 0$), set $P = 0$ and solve for $Q$.

4. Plot these two intercepts on the graph: one at $(0, P)$ and one at $(Q, 0)$.

5. Calculate the slope of the line. The slope is the coefficient of $Q$ in the equation, which tells you how much $P$ decreases as $Q$ increases by 1 unit.

Try solving on your own before revealing the answer!

Final Answer:

The P-intercept is at $(0, 60)$ and the Q-intercept is at $(20, 0)$. The slope of the demand function is $-3$, indicating that for each additional unit of $Q$, $P$ decreases by 3 units. The graph is a straight line connecting these two intercepts.