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Sagot :
Certainly! Let's complete the table step-by-step and then address the calculation of MPC and its interpretation.
Let's fill in the missing values in the table one by one.
1. Identify the given data:
- [tex]\( MPC = 0.97 \)[/tex]
- [tex]\( MPS = 0.03 \)[/tex] (Given directly)
- Relations: [tex]\( S = Y - C \)[/tex], [tex]\( APC = \frac{C}{Y} \)[/tex], [tex]\( APS = \frac{S}{Y} \)[/tex]
We start filling the table with the given [tex]\( MPS \)[/tex] and [tex]\( MPC \)[/tex].
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|} \hline Y & C & S & tPC & APS & MPC & MPS \\ \hline 25 & 25 - S & S & \frac{C}{25} & \frac{S}{25} & 0.97 & 0.03 \\ \hline 50 & 50 - S & 20 & \frac{C}{50} & \frac{20}{50} & 0.97 & 0.03 \\ \hline 75 & 75 - S & 40 & \frac{C}{75} & \frac{40}{75} & 0.97 & 0.03 \\ \hline 100 & 100 - S & 60 & \frac{C}{100} & \frac{60}{100} & 0.97 & 0.03 \\ \hline 125 & 125 - S & 80 & \frac{C}{125} & \frac{80}{125} & 0.97 & 0.03 \\ \hline 150 & 150 - S & 100 & \frac{C}{150} & \frac{100}{150} & 0.97 & 0.03 \\ \hline \end{array} \][/tex]
Next, let's calculate the values of [tex]\( C \)[/tex] considering [tex]\( S \)[/tex]:
1. For [tex]\( Y = 50 \)[/tex]:
[tex]\[ S = 20 \][/tex]
[tex]\[ C = Y - S = 50 - 20 = 30 \][/tex]
[tex]\[ APC = \frac{C}{Y} = \frac{30}{50} = 0.6 \][/tex]
[tex]\[ APS = \frac{S}{Y} = \frac{20}{50} = 0.4 \][/tex]
2. For [tex]\( Y = 75 \)[/tex]:
[tex]\[ S = 40 \][/tex]
[tex]\[ C = Y - S = 75 - 40 = 35 \][/tex]
[tex]\[ APC = \frac{C}{Y} = \frac{35}{75} \approx 0.47 \][/tex]
[tex]\[ APS = \frac{S}{Y} = \frac{40}{75} \approx 0.53 \][/tex]
3. For [tex]\( Y = 100 \)[/tex]:
[tex]\[ S = 60 \][/tex]
[tex]\[ C = Y - S = 100 - 60 = 40 \][/tex]
[tex]\[ APC = \frac{C}{Y} = \frac{40}{100} = 0.4 \][/tex]
[tex]\[ APS = \frac{S}{Y} = \frac{60}{100} = 0.6 \][/tex]
4. For [tex]\( Y = 125 \)[/tex]:
[tex]\[ S = 80 \][/tex]
[tex]\[ C = Y - S = 125 - 80 = 45 \][/tex]
[tex]\[ APC = \frac{C}{Y} = \frac{45}{125} = 0.36 \][/tex]
[tex]\[ APS = \frac{S}{Y} = \frac{80}{125} = 0.64 \][/tex]
5. For [tex]\( Y = 150 \)[/tex]:
[tex]\[ S = 100 \][/tex]
[tex]\[ C = Y - S = 150 - 100 = 50 \][/tex]
[tex]\[ APC = \frac{C}{Y} = \frac{50}{150} \approx 0.33 \][/tex]
[tex]\[ APS = \frac{S}{Y} = \frac{100}{150} \approx 0.67 \][/tex]
Now, let's fill in the table:
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|} \hline Y & C & S & APC & APS & MPC & MPS \\ \hline 25 & 0 & 25 & 0 & 1 & 0.97 & 0.03 \\ \hline 50 & 30 & 20 & 0.6 & 0.4 & 0.97 & 0.03 \\ \hline 75 & 35 & 40 & 0.47 & 0.53 & 0.97 & 0.03 \\ \hline 100 & 40 & 60 & 0.4 & 0.6 & 0.97 & 0.03 \\ \hline 125 & 45 & 80 & 0.36 & 0.64 & 0.97 & 0.03 \\ \hline 150 & 50 & 100 & 0.33 & 0.67 & 0.97 & 0.03 \\ \hline \end{array} \][/tex]
## Q#3b. Given that the MPS of a typical consumer is 0.03, calculate his/her MPC and give its economic interpretation.
Since the Marginal Propensity to Save (MPS) is 0.03, we calculate the Marginal Propensity to Consume (MPC) using the relationship:
[tex]\[ MPC = 1 - MPS \][/tex]
Thus,
[tex]\[ MPC = 1 - 0.03 = 0.97 \][/tex]
### Economic Interpretation:
The Marginal Propensity to Consume (MPC) is 0.97. This means that for every additional dollar of income that a typical consumer receives, they spend 97 cents on consumption and save only 3 cents. Essentially, this high MPC indicates that consumers are more likely to spend the money they earn rather than save it. This behavior can be expected in an economy that is consumer-driven, where people are focusing more on consumption than savings.
Let's fill in the missing values in the table one by one.
1. Identify the given data:
- [tex]\( MPC = 0.97 \)[/tex]
- [tex]\( MPS = 0.03 \)[/tex] (Given directly)
- Relations: [tex]\( S = Y - C \)[/tex], [tex]\( APC = \frac{C}{Y} \)[/tex], [tex]\( APS = \frac{S}{Y} \)[/tex]
We start filling the table with the given [tex]\( MPS \)[/tex] and [tex]\( MPC \)[/tex].
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|} \hline Y & C & S & tPC & APS & MPC & MPS \\ \hline 25 & 25 - S & S & \frac{C}{25} & \frac{S}{25} & 0.97 & 0.03 \\ \hline 50 & 50 - S & 20 & \frac{C}{50} & \frac{20}{50} & 0.97 & 0.03 \\ \hline 75 & 75 - S & 40 & \frac{C}{75} & \frac{40}{75} & 0.97 & 0.03 \\ \hline 100 & 100 - S & 60 & \frac{C}{100} & \frac{60}{100} & 0.97 & 0.03 \\ \hline 125 & 125 - S & 80 & \frac{C}{125} & \frac{80}{125} & 0.97 & 0.03 \\ \hline 150 & 150 - S & 100 & \frac{C}{150} & \frac{100}{150} & 0.97 & 0.03 \\ \hline \end{array} \][/tex]
Next, let's calculate the values of [tex]\( C \)[/tex] considering [tex]\( S \)[/tex]:
1. For [tex]\( Y = 50 \)[/tex]:
[tex]\[ S = 20 \][/tex]
[tex]\[ C = Y - S = 50 - 20 = 30 \][/tex]
[tex]\[ APC = \frac{C}{Y} = \frac{30}{50} = 0.6 \][/tex]
[tex]\[ APS = \frac{S}{Y} = \frac{20}{50} = 0.4 \][/tex]
2. For [tex]\( Y = 75 \)[/tex]:
[tex]\[ S = 40 \][/tex]
[tex]\[ C = Y - S = 75 - 40 = 35 \][/tex]
[tex]\[ APC = \frac{C}{Y} = \frac{35}{75} \approx 0.47 \][/tex]
[tex]\[ APS = \frac{S}{Y} = \frac{40}{75} \approx 0.53 \][/tex]
3. For [tex]\( Y = 100 \)[/tex]:
[tex]\[ S = 60 \][/tex]
[tex]\[ C = Y - S = 100 - 60 = 40 \][/tex]
[tex]\[ APC = \frac{C}{Y} = \frac{40}{100} = 0.4 \][/tex]
[tex]\[ APS = \frac{S}{Y} = \frac{60}{100} = 0.6 \][/tex]
4. For [tex]\( Y = 125 \)[/tex]:
[tex]\[ S = 80 \][/tex]
[tex]\[ C = Y - S = 125 - 80 = 45 \][/tex]
[tex]\[ APC = \frac{C}{Y} = \frac{45}{125} = 0.36 \][/tex]
[tex]\[ APS = \frac{S}{Y} = \frac{80}{125} = 0.64 \][/tex]
5. For [tex]\( Y = 150 \)[/tex]:
[tex]\[ S = 100 \][/tex]
[tex]\[ C = Y - S = 150 - 100 = 50 \][/tex]
[tex]\[ APC = \frac{C}{Y} = \frac{50}{150} \approx 0.33 \][/tex]
[tex]\[ APS = \frac{S}{Y} = \frac{100}{150} \approx 0.67 \][/tex]
Now, let's fill in the table:
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|} \hline Y & C & S & APC & APS & MPC & MPS \\ \hline 25 & 0 & 25 & 0 & 1 & 0.97 & 0.03 \\ \hline 50 & 30 & 20 & 0.6 & 0.4 & 0.97 & 0.03 \\ \hline 75 & 35 & 40 & 0.47 & 0.53 & 0.97 & 0.03 \\ \hline 100 & 40 & 60 & 0.4 & 0.6 & 0.97 & 0.03 \\ \hline 125 & 45 & 80 & 0.36 & 0.64 & 0.97 & 0.03 \\ \hline 150 & 50 & 100 & 0.33 & 0.67 & 0.97 & 0.03 \\ \hline \end{array} \][/tex]
## Q#3b. Given that the MPS of a typical consumer is 0.03, calculate his/her MPC and give its economic interpretation.
Since the Marginal Propensity to Save (MPS) is 0.03, we calculate the Marginal Propensity to Consume (MPC) using the relationship:
[tex]\[ MPC = 1 - MPS \][/tex]
Thus,
[tex]\[ MPC = 1 - 0.03 = 0.97 \][/tex]
### Economic Interpretation:
The Marginal Propensity to Consume (MPC) is 0.97. This means that for every additional dollar of income that a typical consumer receives, they spend 97 cents on consumption and save only 3 cents. Essentially, this high MPC indicates that consumers are more likely to spend the money they earn rather than save it. This behavior can be expected in an economy that is consumer-driven, where people are focusing more on consumption than savings.
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