Chapter 19: Problem 1

How is income determined in a model, where there exists government expenditure, lump sum income taxes and transfer payments? Explain.

Short Answer

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#Short Answer# In a model with government expenditure, lump sum income taxes, and transfer payments, income determination involves the consumption function, government expenditure, tax revenue, and transfer payments. The equilibrium condition is achieved when aggregate expenditure equals national income (AE = Y). The national income in this model is given by the equation Y = (1/(1-c))(C₀ + cT - cTr + G), where Y represents national income, C₀ is autonomous consumption, c is the marginal propensity to consume, T is lump sum income taxes, Tr is transfer payments, and G is government expenditure. The model also takes into account the multiplier effect (1/(1-c)).

Step by step solution

1. Consumption function

The consumption function represents the relationship between consumption and disposable income (Yd), which is the income remaining after paying taxes and receiving transfer payments. In the simple Keynesian model, the consumption function can be given by: C = C₀ + c(Y-T) Where: C = Consumption C₀ = Autonomous consumption (consumption when disposable income is zero) c = Marginal propensity to consume (the fraction of additional income that is spent on consumption) Y = National income T = Lump sum income taxes

2. Government expenditure, transfer payments, and tax revenue

In addition to the consumption function, we need to take into account government expenditure (G), transfer payments, and tax revenue (REC). In a simple model, these can be given by: G: Government expenditure on goods and services (assumed to be fixed) REC: Tax revenue collected through lump sum income taxes Tr: Transfer payments made by the government

3. Aggregate expenditure

Aggregate expenditure (AE) is the sum of consumption, investment, government expenditure, and net exports. In our simple model, we will focus on consumption and government expenditure. Thus, aggregate expenditure can be written as: AE = C + I + G + (X - M) Where: AE = Aggregate expenditure I = Investment (assumed to be exogenously determined) X = Exports M = Imports For our analysis, we can simplify the equation to: AE = C + G

4. Equilibrium condition

The equilibrium condition in the simple Keynesian model is achieved when aggregate expenditure equals national income, i.e., AE = Y We will use this condition to determine the national income in the presence of government expenditure, lump sum income taxes, and transfer payments.

5. Disposable income and equilibrium

First, we need to write down the equation for disposable income (Yd), which is given by: Yd = Y - T + Tr Now, substituting the consumption function and disposable income equation into the aggregate expenditure function, we get: AE = C₀ + c(Y - T + Tr) + G Since, in equilibrium, AE = Y, we can write the equilibrium condition as: Y = C₀ + c(Y - T + Tr) + G

6. Solving for national income

Now we need to solve for Y, the national income: Y - c(Y-T+Tr) = C₀ + G Y(1-c) = C₀ + cT - cTr + G Y = (1/(1-c))(C₀ + cT - cTr + G) Thus, the national income in this model is determined by the autonomous consumption, marginal propensity to consume, government expenditure, lump sum income taxes, transfer payments, and the multiplier effect (1/(1-c)), which captures the impact of additional spending on the overall economy.

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