Question

Suppose the following are national accounts data for a given year for a fictitious country:
$B AUD
Consumption of fixed capital ………………………………………………. 320
Gross private fixed capital formation……………………………………….. 785
Government consumption expenditure………………………………………. 585
Government investment expenditure………………………………………… 210
Imports of goods and services………………………………………………...565
Exports of goods and services………………………………………………...690
Household consumption expenditure………………………………………..3115
Net property and other income paid overseas………………………………….34
Returns to labour…………………………………………………………….2651
Firm profits………………………………………………………………….1687
Other factor rentals……………………………………………………………482
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(j) Suppose that tax revenues are $17 billion for the fiscal year, then what is the value of national savings?
(k) If MPCd remains at 0.63 and GDP changes to $4873 billion; then what will the new level of domestic consumption (i.e. Cdf) be?
(l) If exports then increase by $4 billion, private sector investment decreases by $3 billion; and government consumption and investment decrease and increase by $3 billion and $4 billion respectively: by how much will GDP change and what will be its new value?

Answer 1

National income or GDP has two sides following the way it is calculated. These are income method and expenditure method. Income method measures GDP by adding the income heads, expenditure method calculates GDP by adding the expenditure heads. First we calculate the total income generated using the income method.

Income = returns to labour + firm profits + other factor rentals = 4820

Next we calculate total expenditure by adding the heads of expenditure. And they are broadly categorised as

1. Private Consumption expenditure (by the household) = 3115
2. Private Investment expenditure = gross fixed capital formation = 785
3. Government expenditure (consumption + investment) = 585 + 210 = 795
4. Export – imports = 690 – 565 = 125

Therefore, following expenditure method, GDP can be calculated as 3115 + 785 + 795 + 125 = 4820.

As evident, that the income method and expenditure method yield identical results. Theoretically, this is expressed as the following identity:

C + S + T º C + I + G + (X – M)

Where the left hand side is the income side and the right hand side is the expenditure side; C is private consumption expenditure, S is private savings, T is the amount of tax paid, I is private investment expenditure, G is government expenditure, X is exports and M is imports. From that identity, cancelling and rearranging terms we get, S = I + (G – T) + (X – M) = 785 + (795 – 17) + 125 = 1688.

j) Therefore, the value of national savings is $ 1688 billion.

k) I presume that MPCd refers to domestic marginal propensity to consume. Marginal propensity to consume measure how much consumption increases if income increase by $1. Here income increases by $(4873 – 4820) = $53 billion. Hence, given that MPCd is 0.63, the increase in consumption will be by an amount 0.63 × $53 = $33.39 billion. The new level of domestic consumption will be 3115 + 33.39 = $3148.39 billion

l) If we assume the simplest aggregate demand model where only consumption is a function of income and rest all are lump sum amounts, then expenditure side of the above model can be rewritten as

Y = C₀ + c (Y) + I₀ + G₀ + NX₀           where Y refers to income or GDP, NX refers to net exports and the subscript 0 refers to a constant or given value. c (Y) represents consumption as a function of Y where c^/, the first differentiation of c with respect to Y is positive, implying when income increases by $1, marginal propensity to consume also increases. MPCd is given as 0.63 which implies that at the aggregate level if income increases by $1, consumption increases by $0.63.

A total differentiation of the above equation gives us

dY = dC₀ + c^/dY + dI₀ + dG₀ + dNX₀

or

(1 – c^/) dY = dC₀+ dI₀ + dG₀ + dNX₀

Or

dY = [dC₀+ dI₀ + dG₀ + dNX₀]                                                                          (1)

In the above expression is called the multiplier. If one or more of the constant term in the RHS increases, then income increases by this amount. Since, c^/ is a positive fraction, the multiplier is greater than one, and hence, the increase in income will be more than the increase in the constant term.

1-c)

In the given problem, following changes are mentioned: dNX₀ = 4 billion, dI₀ = - 3 billion, net change in government expenditure is $1 billion, therefore, dG₀ = 1 billion and there is no change in the basic consumption expenditure or dC₀ = 0.

Therefore, in equation the term in the parenthesis = 4 – 3 + 1 = 2.

The multiplier value for c^/ = 0.63 is 2.70 (approximately).

Therefore, change in GDP or dY = 2 × 2.70 = 5.40.

Hence, the new value of GDP will be $(4820 + 5.40) = $ 4825.4 billion.