Answer to Question #200056 in Macroeconomics for Sahej

Question

Assume a simple closed economy without exports and imports. autonomous consumption expenditure is 50 billion. The marginal propensity to consume is 0.6 desired investement is 10 billion and govt pirchase is 20 billion.

Write a mathematical equation expressing Savings as a function os disposable income ?

Answer 1

In the Keynesian macroeconomic theory, the saving function shows the amount of savings in the economy at various possible disposable income levels in the economy. The mathematical form of the saving function is shown below

"S=-A+BYd......"1""

In the equation, "1" above "S" represents the saving level, "Yd" represents the disposable income level, "(-)A" represents the autonomous saving level, the autonomous saving level refers to the amount of savings when disposable income level is equal to zero and as an individual consumes even when his disposable income level is zero, therefore, the autonomous saving level is always negative and equal to the autonomous consumption expenditure(in negative terms). The autonomous consumption expenditure shows the amount of consumption when the disposable income level is zero.

In the above equation, "1" "B" represents the marginal propensity to save and it shows the increase in saving level when disposable income level increases by one unit. As any increase in disposable income is used either for making savings for or for consumption purposes, therefore, the sum of marginal propensity to consume(MPC) and the marginal propensity to save is always equal to one.

In this economy the marginal propensity to consume is equal to 0.6 therefore the value of marginal propensity to save can be calculated as follows

$MPS=1-MPC\\MPS=1-6\\MPS=0.4$

In this economy the value of autonomous consumption expenditure is equal to 50 billion and the value of marginal propensity to save is equal to 0.4 therefore the mathematical equation of saving function can be expressed as follows

$S=(-)50+0.4Yd...(2)$

In the above equation "2" "S" represents the saving and "Yd" represents the disposable income level in the economy.

The equation "2" above shows the mathematical equation of the saving function.