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Chapter 10: Problem 8

Using the Keynesian consumption function, prove numerically that, as the \(M P C\) rises, saving declines.

Short Answer

Expert verified
It's been numerically demonstrated that as the Marginal Propensity to Consume (MPC) increases, saving decreases.

Step by step solution

01

Understand the terms and equations

We can start by setting up the basic Keynesian Consumption Function \(C = \overline{C} + MPC \cdot YD\). Also keep in mind that Saving (S) equals income minus consumption: \(S = YD - C\).
02

Choose numerical values

Let's take a specific numerical example. Suppose \(YD = 100\), \(MPC = 0.8\) initially and \(\overline{C} = 20\). Plug these values into the consumption equation to find consumption: \(C = 20 + 0.8 \times 100 = 100\). Using the saving equation, saving is \(S = 100 - 100 = 0\).
03

Change the MPC

Now, let's increase the MPC to 0.9 and calculate consumption and saving again. Now, \(C = 20 + 0.9 \times 100 = 110\), and the saving is \(S = 100 - 110 = -10\).
04

Analyze the result

From Step 2 to Step 3, as MPC increased from 0.8 to 0.9, consumption increased and saving decreased from 0 to -10. The amount the consumer saves has decreased as MPC rises, which proves our original statement.

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