Consumption:

This section discusses the consumption function of a closed economy, a closed economy is the consideration of an economies income or output in the absence of imports and exports, and Keynes stated the open economy income or output function as follows:

Y=C+I+G+(X–M)

Where Y is income, C is *consumption*, G is the government expenditure, m is imports and X is exports, for the closed economy the model is stated as:

Y=C+I+G

For this case we consider the closed economy function to discuss the consumption function in the economy.

According to Keynes consumption is a function of income, this function depicts that as the level of income increases then the level of consumption also increases, in cases where the income declines then consumption declines, for this reason therefore consumption is a function of income where Keynes specified the model as follows:

C = F(Y)

Consumption

Where C is **consumption** and Y is income, further analysis of the function shows that there is an autonomous value that is not affected by income, further analysis also shows __that__ we consider the disposable income and not the gross income, disposable income of a consumer is the income minus taxes by the government, the model therefore is stated as follows:

C = b1 + b2(Y –T)

Where C is consumption, b1 is autonomous consumption, b2 is the marginal propensity to consume, Y is income and T is tax. Where Y-T gives us the disposable income the model therefore can be presented as follows:

From the above diagram the consumption curve is an upward sloping curve, this means that as the income increases then consumption also increase due the increased disposable income, the autonomous value is that level of consumption that is not affected by income levels, when income levels are zero then the consumption levels are still positive.

The marginal propensity to consume is the slope of the above curve, the marginal propensity to consume value determines how the consumption of a consumer responds to a change in income, the value of the marginal propensity to consume is greater than zero but less than 1, this mean that when income increases all the increase is not used for **consumption** purposes but saved or invested in other income generating projects, that is why the marginal propensity to consume is greater **than** 0 but less than 1.

Further the marginal propensity to consume can be mathematically derived as follows:

From the above diagram if we assume that the original income level is P1 and the consumption level is C!, an increase in income level to P2 then consumption increases to C2, therefore using the marginal propensity function the marginal propensity to consume can be calculated as

Consumption

follows for this example

MPC = (C2-C1)/ (P2–P1)

Therefore the marginal propensity to consume is the change in consumption level divided by the change in the disposable income levels.

Savings:

Savings is the amount of income that is not consumed and consumers prefer to save in banks or invest, when income increases then there is a possibility that savings will increase, Keynes stated that savings is a function of income, for this reason therefore the savings function can be *stated* as follows:

S = F(Y)

Having stated our function above we have to consider the autonomous value of savings and also the marginal propensity to consume, for this reason therefore we can state the savings function as follows:

The above diagram shows the relationship between savings and income, as the level of income increases then the savings level also rises, however when the income level is zero then we expect zero levels of savings, therefore there is a level of income in the economy that allows the consumers to save and if income is below this point then there are zero or even negative savings value.

The savings function can be stated as follows:

Consumption

S = a1 + a2 (Y-T)

Where a is the autonomous value which we expect to be zero or negative, a2 is the marginal propensity to save which is greater than zero but less than 1, Y is income and T is tax, we can calculate the marginal propensity to consume as the change in savings divided by the change in income. This value shows the responsiveness of savings level due to an increase or decline in the level of income.

*Relationship* between savings and income:

This section considers the relationship between savings and consumption, when income increases then the level of savings and *consumption* increases, income is either consumed or saved, for this reason therefore there is a relationship between consumption and savings. When the disposable income of a consumer is determined the consumer will consume a portion of the income and the remaining amount is saved, therefore it is clear that the marginal propensity to consume and the marginal propensity to save have a relationship where if you add the two we get a value one.

MPC+MPS=1

Where MPC is marginal propensity to consume and MPS is marginal propensity to save.

If we assume that a consumer experiences an increase in his income by 100 units, he decides to consume an additional 10 units and save the remaining 90 units. Using this data we can determine the change in income is 100, change in consumption is 10 and the change in savings is 90.

We can determine the marginal propensity to consume as follows:

Consumption

MPC = ∆C/∆Y

MPC = 10/100

Therefore the marginal propensity to consume is 0.1

The marginal propensity to save is determined as follows

MPC = ∆S/∆Y

MPS = 90/100

Therefore the marginal propensity to save is therefore 0.9

For this reason therefore it is clear that when we add the marginal propensity to save and the marginal propensity to consume the value is one, in our case 0.1 + 0.9 = 1, therefore the savings and consumption level are related.

Consumption

References:

Brian Snow (1997) Macroeconomics: Introduction to Macroeconomics, Rout ledge publishers, London

Philip Hardwick (2004) Introduction to Modern Economics, Pearson Press, New York

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