Calculating Marginal Propensity to Save and Marginal Propensity to Consume
Consider the following table. For this hypothetical economy, the marginal propensity to save is constant at all levels of real GDP, and investment spending is autonomous. There is no government.
Real
GDP----Consumption-------Saving-------Investment
($)-------($)-------------($)-----------($)
2,000----2,200-----------------------------
4,000----4,000-----------------------------
6,000----------------------------------------------------------
8,000----------------------------------------------------------
10,000----------------------------------------------------------
12,000----------------------------------------------------------
You need to:
1. Complete the table.
2. Calculate the marginal propensity to save.
3. Calculate the marginal propensity to consume.
4. Draw a graph of the consumption function using the Grapher. Then, add the investment function to obtain C+I.
5. Draw another graph showing the saving and investment curves under the C+I graph. What is the level of real GDP?
6. Calculate the numerical value of the multiplier.
7. Calculate the equilibrium real GDP without investment. What is the multiplier effect from the inclusion of investment?
8. Calculate the average propensity to consume at equilibrium real GDP.
9. If equilibrium real GDP is $8,000 when investment is $400, explain what happens to equilibrium real GDP if autonomous investment declines to $200.
(2) Calculating Average Propensity to Save and Average Propensity to Consume
A nation's consumption function (expressed in millions of inflation-adjusted dollars) is
C=$800 +0.80Y. There are no taxes in this nation.
Now answer the following questions:
1. What is the value of autonomous saving?
2. What is the value of the multiplier?
Take a shot. what do you think.
Hint, S=I, where I is composed of intended or autonomous investment Ia and unintended investment Ib (e.g., change in inventories). Hint 2. Multiplier is 1/MPS
I don't know missing something
Let's start with question (1) and complete the table for the given hypothetical economy:
Real
GDP----Consumption-------Saving-------Investment
($)-------($)-------------($)-----------($)
2,000----2,200-----(-200)-----------------
4,000----4,800-----(-800)-----------------
6,000----7,400----(-1,400)----------------
8,000----9,600----(-1,600)----------------
10,000---11,800---(-1,800)----------------
12,000---14,000---(-2,000)----------------
To calculate the saving column, we can use the formula:
Saving = Real GDP - Consumption - Investment
For question (2), let's calculate the marginal propensity to save (MPS). The MPS measures the change in saving as a result of a change in income.
MPS = Change in Saving / Change in Real GDP
To calculate the change in saving and real GDP, we can use the values from the table:
Change in Saving = Saving at higher GDP - Saving at lower GDP
Change in Real GDP = Higher GDP - Lower GDP
Using the values from the table, we can calculate the MPS for each change in real GDP:
MPS for 2,000 to 4,000 = (-800 - (-200)) / (4,000 - 2,000)
MPS for 4,000 to 6,000 = (-1,400 - (-800)) / (6,000 - 4,000)
MPS for 6,000 to 8,000 = (-1,600 - (-1,400)) / (8,000 - 6,000)
MPS for 8,000 to 10,000 = (-1,800 - (-1,600)) / (10,000 - 8,000)
MPS for 10,000 to 12,000 = (-2,000 - (-1,800)) / (12,000 - 10,000)
Summing up the MPS values calculated above and dividing by the number of changes, we get the marginal propensity to save (MPS):
MPS = (-600 + (-600) + (-200)) / 5
For question (3), let's calculate the marginal propensity to consume (MPC). The MPC measures the change in consumption as a result of a change in income.
MPC = 1 - MPS
Substituting the value of MPS calculated earlier, we have:
MPC = 1 - MPS
Now let's move on to question (4) where we'll draw the consumption function graph using the Grapher and add the investment function to obtain C+I.
Unfortunately, as an AI text-only bot, I cannot draw graphs visually. However, the consumption function graph can be drawn by plotting the real GDP on the x-axis and consumption on the y-axis. The investment function would be a horizontal line representing the level of investment at each level of real GDP. The consumption and investment functions combined would give the C+I graph.
For question (5), let's draw another graph showing the saving and investment curves under the C+I graph. The level of real GDP is given when saving equals investment.
Unfortunately, as an AI text-only bot, I cannot draw graphs visually. However, in the saving and investment graph, the saving curve would be upward-sloping, representing an increase in saving as real GDP increases. The investment curve would be a horizontal line representing the level of investment at each level of real GDP. The equilibrium level of real GDP would be where the saving and investment curves intersect.
For question (6), let's calculate the numerical value of the multiplier. The multiplier measures the total change in real GDP resulting from an initial change in spending (autonomous spending or investment).
The multiplier can be calculated using the formula:
Multiplier = 1 / MPS
Substituting the value of MPS calculated earlier, we have:
Multiplier = 1 / MPS
For question (7), let's calculate the equilibrium real GDP without investment and determine the multiplier effect from the inclusion of investment. Equilibrium real GDP occurs when saving equals investment.
The multiplier effect can be calculated using the formula:
Multiplier Effect = 1 / (1 - MPC)
Substituting the value of MPC calculated earlier, we have:
Multiplier Effect = 1 / (1 - MPC)
For question (8), let's calculate the average propensity to consume (APC) at equilibrium real GDP. The APC measures the proportion of income that is consumed at equilibrium.
APC = Consumption / Real GDP
Substituting the values of consumption and real GDP at equilibrium, we have:
APC = Consumption at equilibrium / Real GDP at equilibrium
For question (9), if the equilibrium real GDP is $8,000 when investment is $400, we need to explain what happens to equilibrium real GDP if autonomous investment declines to $200.
When autonomous investment declines to $200, it means there is a decrease in investment spending. This decrease in investment will lead to a decrease in aggregate demand. As a result, the equilibrium level of real GDP will decrease. The extent of the decrease will depend on the multiplier effect, which we calculated earlier.
So, to determine the new equilibrium level of real GDP, we can calculate the multiplier effect using the formula mentioned earlier and multiply it by the change in investment spending (from $400 to $200). The result will give us the change in real GDP.
I hope this step-by-step explanation helps you understand and complete the calculations.
1. To complete the table, we need to calculate the missing values for consumption and saving at each level of real GDP.
Real
GDP----Consumption-------Saving-------Investment
($)-------($)-------------($)-----------($)
2,000----2,200-----------(-200)-----------------
4,000----4,800-----------(-800)-----------------
6,000----6,400-----------(-400)-----------------
8,000----8,000--------------0-----------------
10,000---9,600-------------400-----------------
12,000--11,200-----------1,200-----------------
2. The marginal propensity to save (MPS) is the change in saving divided by the change in real GDP. To calculate the MPS, we can look at the change in saving between two consecutive levels of real GDP and divide it by the change in real GDP.
MPS = Change in Saving / Change in Real GDP
Using the table, let's calculate the MPS between $6,000 and $8,000.
Change in Saving = $0 - (-400) = $400
Change in Real GDP = $8,000 - $6,000 = $2,000
MPS = 400 / 2,000 = 0.2
Therefore, the marginal propensity to save (MPS) is 0.2.
3. The marginal propensity to consume (MPC) is the change in consumption divided by the change in real GDP. Since we know that the marginal propensity to save (MPS) is constant at all levels of real GDP, the marginal propensity to consume (MPC) can be calculated as:
MPC = 1 - MPS
MPC = 1 - 0.2 = 0.8
Therefore, the marginal propensity to consume (MPC) is 0.8.
4. To draw the consumption function graph, you can use a graphing tool like Grapher. The consumption function equation is given as C = $800 + 0.80Y, where C is consumption and Y is real GDP. In this case, since there is no government, the investment spending is autonomous and does not depend on real GDP. Therefore, the consumption and investment functions can be added together to obtain the aggregate expenditure (C+I) curve.
5. To draw the saving and investment curves under the C+I graph, you can plot the saving and investment values from the table on a graph. The level of real GDP is determined by the intersection of the saving curve and the C+I curve.
6. The numerical value of the multiplier can be calculated using the formula:
Multiplier = 1 / MPS
In this case, the MPS is 0.2, so the multiplier is:
Multiplier = 1 / 0.2 = 5
Therefore, the multiplier is 5.
7. The equilibrium real GDP without investment can be calculated by dividing autonomous consumption by (1 - MPC). In this case, since there is no government, autonomous consumption is the intercept of the consumption function, which is $800.
Equilibrium real GDP without investment = Autonomous Consumption / (1 - MPC)
Equilibrium real GDP without investment = $800 / (1 - 0.8)
Equilibrium real GDP without investment = $800 / 0.2
Equilibrium real GDP without investment = $4,000
The multiplier effect from the inclusion of investment is equal to the multiplier. In this case, the multiplier is 5.
8. The average propensity to consume (APC) at equilibrium real GDP can be calculated as:
APC = Consumption / Equilibrium real GDP
Using the table, let's calculate the APC at equilibrium real GDP of $8,000.
APC = $8,000 / $8,000 = 1
Therefore, the average propensity to consume (APC) at equilibrium real GDP is 1.
9. If equilibrium real GDP is $8,000 when investment is $400, and autonomous investment declines to $200, it means that investment decreases by $200. The decrease in investment would lead to a decrease in aggregate expenditure (C+I), which would result in a decrease in equilibrium real GDP. The magnitude of the decrease in real GDP will depend on the multiplier. In this case, the multiplier is 5, so a $200 decrease in investment would result in a $1,000 decrease in equilibrium real GDP.
Equilibrium real GDP = $8,000 - ($200 * 5) = $8,000 - $1,000 = $7,000
Therefore, if autonomous investment declines to $200, equilibrium real GDP would decrease to $7,000.