Answer to Question #238156 in Macroeconomics for OPPONG

Question

Suppose an economy is described by the following equations.

C=$100 +0.75Y and I =$300

(a) calculate the equilibrium level of national income and graph the aggregate expenditures curve and 45 degree line.

(b) suppose saving increases by $50 at every level of national income. How would the aggregate expenditures curve you drew be affected? explain.c calculate the new equilibrium level of national income.

(c) Calculate the level of savings at the original equilibrium and the the new equilibrium. Does this example demonstrate the paradox of thrift? Explain.

(d). Illustrate the original equilibrium level of national income and the change in the equilibrium level of national income due to the increase in saving form a,b and c above using the saving and investment graph. Explain your graph carefully

Answer 1

Solution:

a.). At equilibrium: Y = AE

Y = C + I

Y = 100 + 0.75Y + 300

Y – 0.75Y = 100 + 300 = 400

0.25Y = 400

Y = 1,600

The equilibrium level of national income (Y) = 1,600

 

The graph for the aggregate expenditure curve and the 45-degree line is as below:

b.). Since saving is equal to the investment, an increase in saving will lead to an increase in investment which will ultimately raise the aggregate demand and the national income. The aggregate expenditure curve will shift to the right to a new equilibrium point where savings is equal to investment.

The new equilibrium is calculated as follows:

At equilibrium: Y = AE

I = 300 + 50 = 350

Y = C + I

Y = 100 + 0.75Y + 350

Y – 0.75Y = 100 + 350 = 450

0.25Y = 450

Y = 1,800

The new equilibrium level of national income (Y) = 1,800

 

c.). The level of savings at the original equilibrium:

Saving = Y – C

Consumption under the old equilibrium:

C = 100 + 0.75(1600) = 100 + 1200 = 1,300

Or saving function: S = -100 + 0.25Y

Saving at the original equilibrium: S = Y – C = 1,600 – 1,300 = 300

S = -100 + 0.25Y = -100 + 0.25(1600) = -100 + 400 = 300

 

Consumption under the new equilibrium:

C = 100 + 0.75(1800) = 100 + 1350 = 1,450

Saving at the new equilibrium: S = Y – C = 1,800 – 1,450 = 350

S = -100 + 0.25Y = -100 + 0.25(1800) = -100 + 450 = 350

 

This example does not demonstrate the paradox of thrift. This is because according to the paradox of thrift, an increase in autonomous saving leads to a decrease in aggregate demand and hence a decrease in national income which will lower total saving in the long run. That is not the case in this situation since an increase in saving has led to an increase in aggregate demand thus increasing both national income and total saving.

 

d.). The increase in saving has shifted the aggregate demand curve to the left to S_2, increasing the national income from the old equilibrium point of 1,600 to a new equilibrium point of 1,800 as shown in the below graph.