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Calculating Real GDP of an economy entails a general summation of the total output produced in an economy. The two main approaches for calculating this output are the Expenditure Approach and the Income approach. The
Income approach focuses on the incomes which accrue from the totality of economic activities carried out within the economy. The expenditure approach on the other hand focuses on the values of total expenditure in the economy as per the different economic units in the country.
This paper gives a mathematical representation of the expenditure approach to calculate the level of GDP and also assesses the effect of changes in some of the variables on the GDP.
Generally, GDP=Consumption + Investment + Government Expenditure + Net Exports
This can be summarized as
Y= C + I + G + NX
However
C=C0 + c1Yd Where Co is the autonomous level of consumption and
C1 is the marginal propensity to consume. Yd is defined as (Y-T) and is called disposable income
I=Io+I1Y Where Io is the autonomous level of investment and I1 the marginal propensity to invest.
G=Go Where Go is the level of government expenditure determined outside the model.
NX = X-M Where X is the level of exports and M the level of imports
M=Mo+m1Y where Mo is autonomous level of exports and m1 the marginal propensity to import
T=Tp where Tp are taxes as determined by government.
Combining the equation gives
Y=co+c1(Y-Tp) +Io+i1Y+Go+ (Xo-(mo+m1Y))
Hence Y= co+Io+Go+Xo-mo – c1Tp/ 1-c1-i1=m1
1-c1-i1=m1
Given that
Autonomous consumption (Co) = 200
autonomous investment (I0) = 200
government spending = 100
export spending (X0) = 100
autonomous import spending (M0) = 100
taxes (Tp) = 0
marginal propensity to consume (c1) = 0.8
marginal propensity to invest (i1) = 0.1
marginal propensity to import (m1) = 0.15
Then
Y= (200+200+100+100-100)/ (1-0.8-0.1+0.15) = 500/0.25=1,600
Exchange rates have significant effects on international trade. This is because they determine how much the local currency is valued in the international markets. Consequently, they affect the levels of imports and exports from the economy.
Appreciation of the exchange rate has the effect of making imports cheaper in the domestic market while exports get expensive in the international markets. Depreciation of exchange rates on the other hand makes imports expensive in the local market while exports get cheaper in the international markets.
In a case where the exchange rates cause autonomous imports to rise from 100 to 200 the GDP changes as shown below.
The new level of Y is
Y= (200+200+100+100-200)/ (1-0.8-0.1+0.15) = 400/0.25=1600
In the initial state the GDP level is 2000 a figure which is 400 higher than after the change in exchange rate. As mentioned above, the exchange rate is a conversion factor or a price relating local currency to international currency.
This being the case, a rise in the autonomous imports would only result from an appreciation of the exchange rate. This is due to the fact that an appreciation in the exchange rate causes imports to be cheaper hence the same amounts used to purchase the autonomous imports can now purchase much more than before.
It should be noted that the change in the GDP occasioned by the change in autonomous imports is much higher than the actual change in autonomous imports. This is due to the multiplier effect on the economy.
In conclusion, exchange rate is an important component in the determination of the growth of GDP especially in economies where international trade contributes to a large portion of the GDP. It is always best to achieve stability of the exchange rates to avoid the scenario described above
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