Questions: The marginal propensity to save of a certain country is given by S'(x)=0.4+0.1 x. Determine the marginal propensity to consume.

The marginal propensity to save of a certain country is given by S'(x)=0.4+0.1 x. Determine the marginal propensity to consume.
Transcript text: The marginal propensity to save of a certain country is given by $S^{\prime}(x)=0.4+0.1 x$. Determine the marginal propensity to consume.
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Solution

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To determine the marginal propensity to consume (MPC), we need to understand the relationship between the marginal propensity to save (MPS) and the MPC. The sum of the marginal propensity to consume and the marginal propensity to save is always equal to 1. This is because any change in income is either consumed or saved.

Given: \[ S^{\prime}(x) = 0.4 + 0.1x \]

The relationship between the marginal propensity to consume and the marginal propensity to save is: \[ C^{\prime}(x) + S^{\prime}(x) = 1 \]

We can solve for \( C^{\prime}(x) \) by substituting the given \( S^{\prime}(x) \) into the equation: \[ C^{\prime}(x) = 1 - S^{\prime}(x) \] \[ C^{\prime}(x) = 1 - (0.4 + 0.1x) \] \[ C^{\prime}(x) = 1 - 0.4 - 0.1x \] \[ C^{\prime}(x) = 0.6 - 0.1x \]

Therefore, the marginal propensity to consume is: \[ C^{\prime}(x) = 0.6 - 0.1x \]

In summary, the marginal propensity to consume is given by the expression \( C^{\prime}(x) = 0.6 - 0.1x \).

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