If the consumption function is C = 0.01Y2 + 0.2Y + 50 calculate MPC and MPS when Y = 30

If the consumption function is C = 0.01Y2 + 0.2Y + 50 calculate MPC and MPS when Y = 30. . If the savings function is given by S = 0.02Y2 − Y + 100 calculate the values of MPS and MPC when Y = 40. Give a brief interpretation of these results.

The Correct Answer and Explanation is :

To analyze the consumption and savings behavior at different income levels, we will calculate the Marginal Propensity to Consume (MPC) and Marginal Propensity to Save (MPS) using the provided functions.

1. When Income (Y) = 30:

• **Consumption Function (C):** C=0.01Y2+0.2Y+50C = 0.01Y^2 + 0.2Y + 50 Substituting Y = 30: calculatorturn0calculator0
• **Savings Function (S):** S=0.02Y2−Y+100S = 0.02Y^2 – Y + 100 Substituting Y = 30: calculatorturn0calculator1
• **Income (Y):** Y=C+SY = C + S Substituting the values of C and S: calculatorturn0calculator2
• **MPC and MPS:** MPC is the change in consumption divided by the change in income, and MPS is the change in savings divided by the change in income. Given that MPC + MPS = 1, we can calculate: calculatorturn0calculator3 calculatorturn0calculator4

2. When Income (Y) = 40:

• **Consumption Function (C):** Substituting Y = 40: calculatorturn0calculator0
• **Savings Function (S):** Substituting Y = 40: calculatorturn0calculator1
• **Income (Y):** Substituting the values of C and S: calculatorturn0calculator2
• **MPC and MPS:** Using the same approach as above: calculatorturn0calculator3 calculatorturn0calculator4

Interpretation:

• **At Y = 30:**
  • MPC = -0.77
  • MPS = 1.77
  These negative values suggest that at an income level of 30, the individual is dissaving, meaning they are spending more than their income and borrowing or depleting savings to finance consumption.
• **At Y = 40:**
  • MPC = 0.25
  • MPS = 0.75
  At this higher income level, the individual is saving a significant portion of their income (75%) and spending the remaining 25%. This indicates a shift from dissaving to saving behavior as income increases.

The relationship between MPC and MPS is crucial in understanding consumer behavior. A higher MPC indicates a greater tendency to consume additional income, while a higher MPS reflects a greater inclination to save. The sum of MPC and MPS always equals 1, as every additional unit of income is either consumed or saved.

These calculations and interpretations are based on the definitions and relationships between consumption, saving, and income in Keynesian economics.