The slope of saving function is equal to:

Question

Accepted Answer

The correct option is 1:

In macroeconomics, the saving function shows the relationship between the level of income (Y) and the level of saving (S). The slope of any function measures the change in the vertical axis variable divided by the change in the horizontal axis variable. For the saving function, the slope is represented by the Marginal Propensity to Save (MPS), which is the change in saving ($\Delta S$) divided by the change in income ($\Delta Y$). The fundamental relationship between income, consumption (C), and saving is given by $Y = C + S$. Since any change in income ($\Delta Y$) is either consumed ($\Delta C$) or saved ($\Delta S$), we have the identity $\Delta Y = \Delta C + \Delta S$. Dividing the entire identity by $\Delta Y$ gives us $1 = \frac{\Delta C}{\Delta Y} + \frac{\Delta S}{\Delta Y}$. We define the Marginal Propensity to Consume (MPC) as $\frac{\Delta C}{\Delta Y}$ and the MPS as $\frac{\Delta S}{\Delta Y}$. Therefore, the relationship is $1 = MPC + MPS$. Since the slope of the saving function is MPS, we can rearrange the equation to find the slope in terms of MPC: $MPS = 1 - MPC$.

The incorrect option is 2: 1-MPS
This option is mathematically equivalent to MPC (since $MPC = 1 - MPS$). While MPC is a crucial component of the macroeconomic model, it represents the slope of the *consumption* function, not the slope of the *saving* function.

The incorrect option is 3: 1-APC
This expression is mathematically equal to the Average Propensity to Save (APS), since $APC + APS = 1$. APS measures the ratio of total saving to total income ($\frac{S}{Y}$), which is not the slope of the saving function but a specific ratio at a point on the curve.

The incorrect option is 4: 1-APS
This expression is mathematically equal to the Average Propensity to Consume (APC), since $APC = 1 - APS$. APC measures the ratio of total consumption to total income ($\frac{C}{Y}$), which, like APS, is an average ratio and does not represent the marginal change or the slope of the function.