In a simple economy with two countries, let us assume that for
country A, marginal propensity to consume is 0.75 and the import
coefficient is 0.25. For the country B, the marginal propensity to
consume is 0.9 and import coefficient is 0.2. Also the autonomous
expenditure for country A is Rs.500and the same for the country B
is Rs 600. Find equilibrium national income of both the countries
using matrix.
Answers
Step-by-step explanation:
Imagine an economy defined by the following:
C = 140 + 0.9 (Yd).
This is the consumption function where 140 is autonomous consumption, 0.9 is the marginal propensity to consume, and Yd is disposable (i.e. after tax income).
Yd = Y- T, where Y is national income (or GDP) and T = Tax Revenues = 0.3Y; note that 0.3 is the average income tax rate.
I = Investment = 400
G = Government spending = 800
X = Exports = 600
M = Imports = 0.15Y
Step 1. Determine the aggregate expenditure function. Using the numbers from above, it is:
AE = C + I + G + X – M
AE = 140 + 0.9(Y – T) + 400 + 800 + 600 – 0.15Y
Step 2. The equation for the 45-degree line is the set of points where GDP or national income on the horizontal axis is equal to aggregate expenditure on the vertical axis. Thus, the equation for the 45-degree line is: AE = Y.
Step 3. The next step is to solve these two equations for Y (or AE, since they will be equal to each other). Substitute Y for AE:
Y = AE = 140 + 0.9(Y – T) + 400 + 800 + 600 – 0.15Y
Step 4. Insert the term 0.3Y for the tax rate T. This produces an equation with only one variable, Y.
Step 5. Work through the algebra and solve for Y.
Y = 140 + 0.9(Y – 0.3Y) + 400 + 800 + 600 – 0.15Y
Y = 140 + 0.9Y –0.27Y + 1800 – 0.15Y
Y = 1940 + 0.48Y
Y – 0.48Y = 1940
0.52Y = 1940
0.52
Y
0.52
=
1940
0.52
Y = 3730
This algebraic framework is flexible and useful in predicting how economic events and policy actions will affect real GDP.
Say, for example, that because of changes in the relative prices of domestic and foreign goods, the marginal propensity to import falls to 0.1. Calculate the equilibrium output when the marginal propensity to import is changed to 0.10.
Y = 140 + 0.9(Y – 0.3Y) + 400 + 800 + 600 – 0.1Y
Y = 1940 – 0.53Y
0.47Y = 1940
Y = 4127
Alternatively, suppose because of a surge of business confidence, investment rises to 500. Calculate the equilibrium output.
Y = 140 + 0.9(Y – 0.3Y) + 500 + 800 + 600 – 0.15Y
Y = 2040 + 0.48Y
Y – 0.48Y = 2040
0.52Y = 2040
Y = 3923
EXERCISE: CONSUMPTION IN THE INCOME-EXPENDITURE MODEL
Let’s work through another example. Suppose that the amount of autonomous consumption is $20. Assume that taxes are 0.2 of real GDP. Let the marginal propensity to save of after-tax income be 0.1. The level of investment is $70, the level of government spending is $80, and the level of exports is $50. Imports are 0.2 of after-tax income. Given these values, you need to complete the table and then answer these questions: What is the consumption function? What is the equilibrium? Why is a national income of $300 not at equilibrium? How do expenditures and output compare at this point?