Question

Choose the correct consumption function from the options given below with reference to the illustrated diagram.

• A. \(C = 50 + 0.7Y\)
• B. \(C = 100 + 0.8Y\)
• C. \(C = 100 + 0.7Y\)
• D. \(C = 100 + 0.8Y\)

Hint:

In a consumption function, the intercept gives autonomous consumption and the slope gives MPC (rate of change of consumption with income).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The linear consumption function is expressed as \(C = \bar{C} + bY\), where \(\bar{C}\) is autonomous consumption (consumption at zero income) and \(b\) is the Marginal Propensity to Consume (MPC).
Step 2: Key Formula or Approach:
1. Identify the intercept on the Y-axis (\(\bar{C}\)).
2. Calculate \(MPC (b) = \frac{\Delta C}{\Delta Y}\) using two points from the graph.
Step 3: Detailed Explanation:
From the provided graph:
1. At \(Y = 0\), the Consumption line starts at 100. Thus, \(\bar{C} = 100\).
2. At Point \(E\) (Break-even point), Consumption equals Income. Here, \(Y = 500\) and \(C = 500\).
3. Using the formula \(C = \bar{C} + bY\):
\[ 500 = 100 + b(500) \]
\[ 400 = 500b \]
\[ b = \frac{400}{500} = 0.8 \]
The consumption function is \(C = 100 + 0.8Y\).
Step 4: Final Answer:
Based on the intercept and the slope calculated from the break-even point, the correct function is \(C = 100 + 0.8Y\).