Consumption And Investment, Government Expenditure

3 If Consumption C 150 8y Investment I 35 Govt Expendit

Given the following economic data: Consumption function C = 150 + 0.8Y, investment I = $35, government expenditures G = $40, exports X = $15, and imports M = $10, we are tasked with determining various levels of aggregate expenditure and equilibrium income based on different income levels and investment scenarios.

Specifically, the assignment requests:

  1. Calculate the aggregate expenditures when income (Y) is $1,000.
  2. Calculate the aggregate expenditures when income (Y) is $1,200.
  3. Determine the equilibrium level of income where aggregate output equals aggregate expenditures, using the equation Y = C + I + G + X – M.
  4. When investment increases by $10 (to $45), compute the new equilibrium income.
  5. Calculate the spending multiplier associated with this change in investment.

Paper For Above instruction

The macroeconomic analysis of aggregate expenditures and equilibrium income is fundamental to understanding economic fluctuations and policy impacts. The problem set provided involves calculations based on the consumption function, government expenditures, exports, imports, and investment levels, demonstrating typical applications of Keynesian macroeconomic theory.

Calculating Aggregate Expenditures at Different Income Levels

The aggregate expenditure (AE) is the total amount spent on the economy's goods and services at a given level of income. It encompasses consumption (C), investment (I), government spending (G), net exports (X – M), and any autonomous consumption components.

The consumption function is C = 150 + 0.8Y, indicating that consumers spend $150 plus 80% of their income. With fixed investment of $35, government expenditure at $40, exports of $15, and imports of $10, the formula for aggregate expenditure becomes:

  • AE = C + I + G + (X – M) = (150 + 0.8Y) + 35 + 40 + (15 – 10).

Calculating the net exports component: 15 – 10 = 5.

Inserting this into the AE formula results in:

  • AE = 150 + 0.8Y + 35 + 40 + 5 = 230 + 0.8Y.

This formula allows us to evaluate the total aggregate expenditure at specific income levels.

Part A: Aggregate Expenditure at Y = $1,000

Substituting Y = 1000 into the AE formula:

  • AE = 230 + 0.8(1000) = 230 + 800 = $1030.

Part B: Aggregate Expenditure at Y = $1,200

Substituting Y = 1200:

  • AE = 230 + 0.8(1200) = 230 + 960 = $1190.

Determining the Equilibrium Level of Income

The equilibrium level of income occurs where aggregate output (Y) equals aggregate expenditure (AE). Setting Y = AE:

Y = 230 + 0.8Y

Solve for Y:

Y – 0.8Y = 230
0.2Y = 230
Y = 230 / 0.2 = 1150

The equilibrium income is therefore $1,150.

Part D: Effect of Increased Investment

Suppose investment increases by $10, from $35 to $45. The new AE function becomes:

  • AE = 150 + 0.8Y + 45 + 40 + 5 = 240 + 0.8Y.

Finding the new equilibrium:

Y = 240 + 0.8Y
Y – 0.8Y = 240
0.2Y = 240
Y = 240 / 0.2 = 1200

The new equilibrium income increases to $1,200, reflecting the multiplier effect of investment changes.

Calculating the Spending Multiplier

The multiplier effect quantifies how much national income responds to changes in autonomous spending components such as investment. It is calculated as:

Multiplier = 1 / (1 – MPC) = 1 / (1 – 0.8) = 1 / 0.2 = 5

Thus, a $10 increase in investment results in a $50 increase in equilibrium income, consistent with the calculated change from $1,150 to $1,200.

Conclusion

This analysis illustrates core Keynesian macroeconomic principles, emphasizing how autonomous spending influences overall economic activity. The calculations highlight the significance of the marginal propensity to consume and how shocks to investment produce amplified effects through the multiplier mechanism.

References

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