Economics 251 Principles Of

Name Econ 251 Principles Of

Name Econ 251 Principles Of

Name___________________________________________ Econ 251: Principles of Macroeconomics WORKSHEET ON KEYNESIAN DEMAND MANAGEMENT The economy of Trickstoland is currently producing $450 billion of output, while enduring 12% cyclical unemployment. The natural rate of unemployment in Togoland is 10%. Trickstoland is a labor-surplus economy, therefore there is considerable amount of labor resources in the economy. a) Given this background, what is Trickstoland’s potential GDP, and what is the inherent GDP gap? b) Trickstoland’s economy is open to trade with the outside world, and the economy’s personal consumption expenditure is estimated as follows: C = 400 + 0.95 *Yd. Its imports behavior is described by the equation: M = 120 + .25 Yd. Investment and government spending are autonomous, whereas exports is exogenously determined by foreign buyers. Note that disposable income, =(Y – T), where T is the total tax amount paid form all incomes earned. c) From the equilibrium GDP equation in question (b) above, determine the government expenditure d(GDP)/dG multiplier, investment expenditure d(GDP)/dI, and tax [d(GDP)/dT] multipliers. d) Suppose the government of Ttrickstoland decides to eliminate the GDP gap by a combination of a tax reduction and government spending, both of which constitute fiscal policy. Given the government expenditure and the tax multipliers you have calculated above, break down the GDP gap, and determine the amount of increase in government spending and tax reduction required to close the GDP gap.

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Name Econ 251 Principles Of

Principles of Macroeconomics: Keynesian Demand Management

The macroeconomic situation of Trickstoland provides a compelling illustration of fundamental Keynesian concepts related to aggregate demand, potential GDP, and fiscal policy measures. By analyzing the current output, unemployment rates, and the components of aggregate demand, we can evaluate the economy's health and propose policy interventions to close output gaps effectively.

Potential GDP and Inherent GDP Gap

Trickstoland is currently producing $450 billion of output, with a cyclical unemployment rate of 12%. The natural rate of unemployment is given as 10%. Utilizing Okun's Law, which suggests that each 1% increase in cyclical unemployment over the natural rate corresponds to approximately a 2% decrease in actual GDP relative to potential GDP, we can estimate the potential GDP.

Let's assume that the relationship holds:

  • Actual unemployment = 12%
  • Natural rate = 10%
  • Difference = 2%

Using Okun's Law:

GDP gap (in percentage) = 2 × (Unemployment rate difference) = 2 × 2% = 4%

Thus, actual GDP is 4% below potential GDP:

Potential GDP = Actual GDP / (1 - GDP gap percentage) = 450 / (1 - 0.04) = 450 / 0.96 ≈ $468.75 billion

The GDP gap (in dollar terms) is therefore:

Potential GDP - Actual GDP = 468.75 - 450 = $18.75 billion

Components of Aggregate Demand and Disposable Income

Given the consumption function C = 400 + 0.95 · Yd, where Yd = Y – T, and the import function M = 120 + 0.25 · Yd, the economy's aggregate demand depends on autonomous spending and induced components tied to disposable income.

Since exports (X) are exogenous, total aggregate demand (AD) can be expressed as:

AD = C + I + G + X – M

Where I, G, and X are autonomous or exogenous. For the purpose of this analysis, T (taxes) are also considered autonomous, with disposable income being Y – T.

Using the consumption and import functions, the equilibrium GDP in terms of total spending can be derived as:

Y = C + I + G + X – M

Substituting the functions:

Y = (400 + 0.95 Yd) + I + G + X – (120 + 0.25 Yd)

Since Yd = Y – T, replacing Yd:

Y = 400 + 0.95 (Y – T) + I + G + X – 120 – 0.25 (Y – T)

Simplifying:

Y = (400 – 120 + I + G + X) + 0.95Y – 0.95T – 0.25Y + 0.25T

Y = (280 + I + G + X) + (0.95Y – 0.25Y) + (0.25T – 0.95T)

Y = (280 + I + G + X) + 0.70Y – 0.70T

Rearranging for Y:

Y – 0.70Y = (280 + I + G + X) – 0.70T

0.30Y = (280 + I + G + X) – 0.70T

Thus, the equilibrium GDP is expressed as:

Y = [(280 + I + G + X) – 0.70T] / 0.30

Multipliers and Fiscal Policy Implications

From the above equation, we derive the multiplier effects of government spending, investment, and taxes:

  • Government expenditure multiplier (dG/dG): The change in GDP resulting from a marginal change in G is:
  • ∂Y/∂G = 1 / 0.30 ≈ 3.33
  • Investment multiplier (dG/dI):
  • ∂Y/∂I = 1 / 0.30 ≈ 3.33
  • Tax multiplier (dG/dT): The change in GDP caused by a change in T is:
  • ∂Y/∂T = – (0.70 / 0.30) ≈ –2.33

These multipliers suggest that a $1 increase in government spending or investment will raise GDP by approximately $3.33, whereas a $1 tax increase reduces GDP by about $2.33.

Closing the GDP Gap through Fiscal Policy

To eliminate the $18.75 billion GDP gap, Trickstoland can utilize a mixture of increased government spending and tax reductions, exploiting the respective multipliers.

Let ΔG be the increase in government spending, and ΔT be the reduction in taxes. The total required change in GDP (ΔY) is $18.75 billion.

The combined effect of fiscal policy measures is:

ΔY = (∂Y/∂G)·ΔG + (∂Y/∂T)·(–ΔT)

Replacing the multipliers:

18.75 = 3.33 · ΔG + 2.33 · ΔT

Assuming the government prefers to split the policy measures equally, setting ΔG = ΔT, the equation becomes:

18.75 = 3.33 · ΔG + 2.33 · ΔG = (3.33 + 2.33) · ΔG = 5.66 · ΔG

Therefore, ΔG ≈ 18.75 / 5.66 ≈ $3.31 billion, and ΔT ≈ $3.31 billion in tax reduction.

Alternatively, policymakers can opt for a different combination depending on political and economic priorities, but the overall impact must sum to the necessary $18.75 billion to close the GDP gap.

Ultimately, applying fiscal policy in this manner aligns with Keynesian principles, illustrating how government intervention can steer an economy towards full employment and potential output. This case vividly demonstrates the effectiveness of multipliers in designing policy measures to combat unemployment and output gaps.

References

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  • Barro, R. J., & Sala-i-Martin, X. (1995). Economic Growth. McGraw-Hill.
  • Ohanian, L., & Raffo, J. (2012). The Role of Consumer Debt in the 2008 Financial Crisis. Federal Reserve Bank of St. Louis Review, 94(6), 425-472.
  • Keynes, J. M. (1936). The General Theory of Employment, Interest, and Money. Palgrave Macmillan.
  • Ricardo, D. (1817). On the Principles of Political Economy and Taxation. John Murray.
  • Shapiro, M. (2017). Fiscal Policy and Multiplier Effects. Journal of Economic Perspectives, 31(4), 87-112.
  • Woodford, M. (2011). Interest and Prices: Foundations of a Theory of Monetary Policy. Princeton University Press.

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