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Consumption Demand Function
Let us suppose that an empirically estimated linear aggregate consumption function is given as:
C = 200 + 0.75Y
The consumption function is presented as consumption (C) equals $200 even when Y = 0. This consumption is assumed to be financed out of past savings. It shows that the subsequent increases in income (ΔCs) at a fixed proportion of 75%. That is, aggregate consumption increase with the increase in the aggregate income, ata constant rate of 75% of the marginal income. For example, when aggregate income increases from $ 200 to $300, aggregate consumption increases from $250 to %325. Here,
ΔY = 300 – 200 = 100
Therefore, ΔC = 325 – 250 = 75
ΔC/ ΔY = 75/100 = 0.75 (for75%)
And, when income (Y) increases from $300 to $ 400, C increases from $325 to $400. In this case,
ΔY = 400 – 300 = 100
ΔC = 400 – 325 = 75
And, ΔC/ ΔY = 75/100 = 0.75 (or75%)
This shows that, in our example, the marginal propensity to consume (MPC) is constant at 75% at the aggregate level.
Average propensity to consume (APC)
The average propensity to consume (APC) is defined as
APC = C/Y
Given the consumption function, C = a + bY
APC = a +bY/Y
If the consumption function is assumed to be of the form C = bY, then,
APC = bY/Y = b
It implies that if C = bY, then APC = MPC
Saving function
The saving function is the counterpart of the consumption function. It states the relationship between income and saving. Therefore, saving is also the function of disposable income. That is,
S = ƒ(Y)
We know that Y = C + S. thus, consumption and saving functions are counterparts of one another. Therefore, if one of the functions is known, the other can be easily derived. Given the consumption function as C = a + bY, saving function can be easily derived as follows. Since Y = C + S, savings (S) can be defined as:
S = Y – C
By substituting consumption function, C = a + bY, for C, we get
S = Y – (a + bY)
= -a + (1 – b)Y
The term 1 – b in function gives the marginal propensity to save (MPS), where b = MPC = ΔC/ ΔY
The saving function can be derived algebraically as follows. By substituting consumption function, C = 200 + 0.75Y for C, we get the saving function as:
S = Y – (200 + 0.75Y)
= y – 200 – 0.75Y
= -200 + (1 – 0.75)Y
= -200 + 0.25Y
The saving function is presented where savings are negative till income rises to $800. At income of $800, savings equal to zero. Positive savings take place only after income rises above $800. Savings increase at the rate of 25% of the marginal income.
Aggregate demand function
Now that the consumption and saving functions, we can present aggregate demand function, assuming that investment (I) remains constant. Recall aggregate demand (AD) and consumption (C) functions given as:
{AD = C + I⁻: C = a + bY}
By substituting a + bY for C, we get
AD = a + b + I⁻
Recall our estimated hypothetical consumption function C = 200 + 0.75Y and assume that I⁻ = 100. By substitution, the estimated aggregate demand function can be written as:
AD = 200 + 0.75Y + 100
The derivation of the aggregate demand function in constant investment is shown by a horizontal line I⁻ = 100. Consumption (C) being a rising function of income is shown by upward sloping line, C = 200 + 0.75Y. the aggregate demand function is obtained by vertical summation of the consumption function and the constant investment, that is, AD = C + I⁻ = 100, at different levels of income (Y).
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C = 200 + 0.75Y
The consumption function is presented as consumption (C) equals $200 even when Y = 0. This consumption is assumed to be financed out of past savings. It shows that the subsequent increases in income (ΔCs) at a fixed proportion of 75%. That is, aggregate consumption increase with the increase in the aggregate income, ata constant rate of 75% of the marginal income. For example, when aggregate income increases from $ 200 to $300, aggregate consumption increases from $250 to %325. Here,
ΔY = 300 – 200 = 100
Therefore, ΔC = 325 – 250 = 75
ΔC/ ΔY = 75/100 = 0.75 (for75%)
And, when income (Y) increases from $300 to $ 400, C increases from $325 to $400. In this case,
ΔY = 400 – 300 = 100
ΔC = 400 – 325 = 75
And, ΔC/ ΔY = 75/100 = 0.75 (or75%)
This shows that, in our example, the marginal propensity to consume (MPC) is constant at 75% at the aggregate level.
Average propensity to consume (APC)
The average propensity to consume (APC) is defined as
APC = C/Y
Given the consumption function, C = a + bY
APC = a +bY/Y
If the consumption function is assumed to be of the form C = bY, then,
APC = bY/Y = b
It implies that if C = bY, then APC = MPC
Saving function
The saving function is the counterpart of the consumption function. It states the relationship between income and saving. Therefore, saving is also the function of disposable income. That is,
S = ƒ(Y)
We know that Y = C + S. thus, consumption and saving functions are counterparts of one another. Therefore, if one of the functions is known, the other can be easily derived. Given the consumption function as C = a + bY, saving function can be easily derived as follows. Since Y = C + S, savings (S) can be defined as:
S = Y – C
By substituting consumption function, C = a + bY, for C, we get
S = Y – (a + bY)
= -a + (1 – b)Y
The term 1 – b in function gives the marginal propensity to save (MPS), where b = MPC = ΔC/ ΔY
The saving function can be derived algebraically as follows. By substituting consumption function, C = 200 + 0.75Y for C, we get the saving function as:
S = Y – (200 + 0.75Y)
= y – 200 – 0.75Y
= -200 + (1 – 0.75)Y
= -200 + 0.25Y
The saving function is presented where savings are negative till income rises to $800. At income of $800, savings equal to zero. Positive savings take place only after income rises above $800. Savings increase at the rate of 25% of the marginal income.
Aggregate demand function
Now that the consumption and saving functions, we can present aggregate demand function, assuming that investment (I) remains constant. Recall aggregate demand (AD) and consumption (C) functions given as:
{AD = C + I⁻: C = a + bY}
By substituting a + bY for C, we get
AD = a + b + I⁻
Recall our estimated hypothetical consumption function C = 200 + 0.75Y and assume that I⁻ = 100. By substitution, the estimated aggregate demand function can be written as:
AD = 200 + 0.75Y + 100
The derivation of the aggregate demand function in constant investment is shown by a horizontal line I⁻ = 100. Consumption (C) being a rising function of income is shown by upward sloping line, C = 200 + 0.75Y. the aggregate demand function is obtained by vertical summation of the consumption function and the constant investment, that is, AD = C + I⁻ = 100, at different levels of income (Y).
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