Question

Assume an economy where there is an injection of $2,000 of government spending (G) in buying domestic production, and its net exports (NX) are −$400. This economy has a marginal propensity to import (m) of 0.6 , a marginal propensity to consume of 0.3 , and a tax rate of 0.3 .

a. What is the Expenditure function for this economy?
b. What is the slope of the aggregate demand function in this economy?
c. What is the expenditure multiplier for this economy?
d. How much will increase the national income due to the injection in the economy?
e. When will this economy restore its equilibrium?

Answer 1

The expenditure function is calculated by adding up the components of aggregate expenditures and subtracting imports. The slope of the aggregate demand function is determined by the coefficient of national income in the expenditure function. The expenditure multiplier can be found by taking the reciprocal of the slope of the aggregate demand function.

Step-by-step explanation:

a. To determine the expenditure function, we need to add up the components of aggregate expenditures: Consumption (C), Investment (I), Government spending (G), and Exports (X), and subtract Imports (M). The equation for the expenditure function is:

AE = C + I + G + X - M

Where C = 140 + 0.9(Y - T), I = 400, G = 800, X = 600, and M = mY, where m is the marginal propensity to import. Plugging in the values, the expenditure function is:

AE = 140 + 0.9(Y - 0.3Y) + 400 + 800 + 600 - 0.6Y

b. The slope of the aggregate demand function can be determined by looking at the coefficient of Y in the expenditure function. In this case, the coefficient of Y is 1 - 0.9 - 0.6 = -0.5. Therefore, the slope of the aggregate demand function is -0.5.

c. The expenditure multiplier can be calculated by taking the reciprocal of the slope of the aggregate demand function. In this case, the expenditure multiplier is 1 / (-0.5) = -2.

d. To find the increase in national income, we can multiply the injection of government spending by the expenditure multiplier. In this case, the increase in national income is $2,000 * -2 = -$4,000.

e. The economy will restore its equilibrium when the level of aggregate expenditure equals the level of national income. This occurs when Aggregate Expenditure (AE) = Y. Using the expenditure function, we can set AE equal to Y and solve for the equilibrium level of national income. However, this information is not provided in the question.