Consider the following consumption function. C = 200 + .75(DPI),

Where C is consumption, autonomous spending is 200, the MPC is .75, and DPI is disposable personal income.

Using the Graph below, graph the Consumption Function.

C

100
0 = Income

On the Graph, label the point where Savings = 0, as well as the areas of saving and dissaving.
Now, derive the point where Savings = 0 using the formulas. What is consumption when savings is zero?

What happens if autonomous spending increases to 300, so C= 300 + .75(DPI)? Show on the graph, and solve for the savings = 0 income below.

7. Consider the following Data:
MPS = .2
Autonomous spending is 100

What is the consumption function?

To graph the consumption function, we need to plot the relationship between consumption (C) and disposable personal income (DPI).

1. Start by drawing a vertical axis labeled "C" for consumption and a horizontal axis labeled "DPI" for disposable personal income.

2. The consumption function is given as C = 200 + 0.75(DPI). This means that consumption is equal to 200 plus 0.75 times the disposable personal income.

3. Plot the point (0, 200) on the graph to represent the autonomous spending of 200 when the disposable personal income is zero.

4. To find additional points, choose different values for DPI and calculate the corresponding consumption using the consumption function. For example, if DPI is 100, then C = 200 + 0.75(100) = 275. Plot this point on the graph.

5. Connect the plotted points with a line to represent the consumption function.

To label the point where savings equal zero and the areas of saving and dissaving:

1. Find the point where savings equal zero by locating the intersection of the consumption function and the 45-degree line. The 45-degree line represents the equality of consumption and income. At this point, consumption equals disposable personal income, so there is no saving. Label this point on the graph.

2. Above this point, where consumption exceeds income, there is dissaving. Below this point, where income exceeds consumption, there is saving. Label these areas on the graph.

To derive the point where savings equal zero using the formulas:

1. Set the consumption function equal to disposable personal income: C = DPI.

2. Substitute the consumption function C = 200 + 0.75(DPI) into the equation: 200 + 0.75(DPI) = DPI.

3. Solve for DPI: 0.25(DPI) = 200.

4. Divide both sides by 0.25: DPI = 800.

5. The point where savings equal zero occurs at DPI = 800. At this point, consumption is 200 + 0.75(800) = 800.

If autonomous spending increases to 300, the new consumption function becomes C = 300 + 0.75(DPI).

To show this on the graph, plot the point (0, 300) to represent the autonomous spending of 300 when DPI is zero. Then, calculate and plot additional points using different values for DPI.

To solve for the income where savings equal zero:

1. Set the consumption function equal to disposable personal income: C = DPI.

2. Substitute the new consumption function C = 300 + 0.75(DPI) into the equation: 300 + 0.75(DPI) = DPI.

3. Solve for DPI: 0.25(DPI) = 300.

4. Divide both sides by 0.25: DPI = 1200.

5. The point where savings equal zero occurs at DPI = 1200. At this point, consumption is 300 + 0.75(1200) = 1200.

If the MPS (marginal propensity to save) is 0.2 and the autonomous spending is 100, the consumption function can be derived as follows:

1. The MPS is the proportion of additional income saved, which means the MPC (marginal propensity to consume) is 1 - MPS = 1 - 0.2 = 0.8.

2. The consumption function is given as C = autonomous spending + MPC * DPI.

3. Substitute the given values: C = 100 + 0.8(DPI).

Therefore, the consumption function is C = 100 + 0.8(DPI).