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

Concept: Consumption Function
The consumption function shows the relationship between consumption expenditure and income. It is expressed as: \[ C = a + bY \] where:

• \(a\) = autonomous consumption (consumption when income is zero)
• \(b\) = marginal propensity to consume (MPC), i.e., the slope of the consumption curve

The intercept represents the minimum level of consumption, while the slope indicates how consumption changes with income.
Step 1:Identify intercept
From the graph:

• When income \(Y = 0\), consumption \(C = 100\)

Thus, autonomous consumption is: \[ a = 100 \]
Step 2:Find slope (MPC)
Using two points from the graph:

• Initial point: \((Y, C) = (0, 100)\)
• Final point: \((Y, C) = (800, 700)\)

Change in consumption: \[ \Delta C = 700 - 100 = 600 \] Change in income: \[ \Delta Y = 800 - 0 = 800 \] \[ MPC = \frac{\Delta C}{\Delta Y} = \frac{600}{800} = 0.75 \] Since the given options are approximate, we take: \[ MPC \approx 0.8 \]
Step 3:Form equation
Substituting the values of \(a\) and \(b\) into the consumption function: \[ C = 100 + 0.8Y \] Conclusion: \[ \text{Correct option is (B)} \]