Question

Fill in the blanks in the following table: Income Consumption Saving MPC MPS APC APS $$ \begin{array}{llll} \$ 1,000 & \$ 400 & & \\ \$ 2,000 & \$ 900 & \$ 1,100 \\ \$ 3,000 & \$ 1,400 & & .60 \\ \$ 4,000 & & \$ 2,100 & \end{array} $$

Short answer

Answer: When income is $3,000, the marginal propensity to consume (MPC) is 0.6, and the marginal propensity to save (MPS) is 0.4.

Step-by-step solution

Understand the definitions and formulas of MPC, MPS, APC, and APS

MPC is the proportion of an additional dollar of income that is spent on consumption. The formula for MPC is: $$ MPC = \frac{\Delta C}{\Delta Y}$$ MPS is the proportion of an additional dollar of income that is saved. The formula for MPS is: $$ MPS = \frac{\Delta S}{\Delta Y}$$ APC is the proportion of total income that is spent on consumption. The formula for APC is: $$APC = \frac{C}{Y}$$ APS is the proportion of total income that is saved. The formula for APS is: $$APS = \frac{S}{Y}$$

Calculate the missing values for Saving,

We are given in the first row that Consumption is \(400 when Income is \)1000. Therefore, the Saving in the first row is calculated as: $$Saving = Income - Consumption$$ $$S_1 = \$1000 - \$400 = \$600$$ In the third row, the MPS is given as $0.60. To find the missing value for Saving, we can use the formula MPS: $$ MPS = \frac{\Delta S}{\Delta Y}$$ $$0.60 = \frac{S_3 - S_2}{\$3000 - \$2000}$$ $$0.60 = \frac{S_3 - \$1100}{\$1000}$$ $$S_3 = 0.60 \times \$1000 + \$1100 = \$1600$$ The given table now looks like this: $$ \begin{array}{llll} \$ 1,000 & \$ 400 & \$ 600 \\\ \$ 2,000 & \$ 900 & \$ 1,100 \\\ \$ 3,000 & \$ 1,400 & \$ 1,600 & .60 \\\ \$ 4,000 & & \$ 2,100 & \end{array} $$

Calculate the missing values for Consumption,

We are only missing Consumption in the last row, which we can calculate using the Saving value: $$Consumption = Income - Saving$$ $$C_4 = \$4000 - \$2100 = \$1900$$ Now, all the Consumption and Saving values are filled in: $$ \begin{array}{llll} \$ 1,000 & \$ 400 & \$ 600 \\\ \$ 2,000 & \$ 900 & \$ 1,100 \\\ \$ 3,000 & \$ 1,400 & \$ 1,600 & .60 \\\ \$ 4,000 & \$ 1900 & \$ 2,100 & \end{array} $$

Calculate the missing values for MPC, MPS, APC, and APS

First, calculate MPC and MPS for all rows except the last one: $$MPC_{row 1} = \frac{\Delta C_1}{\Delta Y_1} = \frac{(\$ 900 - \$ 400)}{(\$2000 - \$ 1000)} = \frac{\$ 500}{\$1000} = 0.5$$ $$MPC_{row 2} = \frac{\Delta C_2}{\Delta Y_2}= \frac{\$ 1900-\$ 900}{\$ 4000 - \$2000}= \frac{1000}{2000} = 0.5$$ $$MPS_{row 1} = \frac{\Delta S_1}{\Delta Y_1} = 1- MPC_{row 1}= 1-0.5 = 0.5$$ $$MPS_{row 2} = 1-MPC_{row 2} = 1- 0.5 = 0.5 $$ Now, calculate APC and APS for all four rows: $$APC_1 = \frac{\$ 400}{\$ 1,000} = 0.4$$ $$APS_1 = 1 - APC_1 = 1-0.4 = 0.6$$ $$A$$ $$APC_2 = \frac{\$ 900}{\$ 2,000} = 0.45$$ $$APS_2 = 1 - APC_2 = 1-0.45 = 0.55$$ $$APC_3 = \frac{\$ 1,400}{\$ 3,000} = 0.4667$$ $$APS_3 = 1 - APC_3 = 1-0.4667 = 0.5333$$ $$APC_4 = \frac{\$ 1,900}{\$ 4,000} = 0.475$$ $$APS_4 = 1 - APC_4 = 1-0.475 = 0.525$$ Finally, we can put all the values back in the table: $$ \begin{array}{llll} \$ 1,000 & \$ 400 & \$ 600 & 0.5 & 0.5 & 0.4 & 0.6 \\\ \$ 2,000 & \$ 900 & \$ 1,100 & 0.5 & 0.5 & 0.45 & 0.55 \\\ \$ 3,000 & \$ 1,400 & \$ 1,600 & .60 & .40 & .4667 & .5333 \\\ \$ 4,000 & \$ 1,900 & \$ 2,100 & 0.5 & 0.5 & .475 & .525 \end{array} $$