Question

1. What is the multiplier if households have an MPC of 0.6?
2. Create a table similar to Figure 10.8 in your textbook. Assume that the households have an MPC of 0.80 and there is a $9 billion increase to investment spending.

	Change in income	Change in consumption	Change in savings
Round 1
Round 2
Round 3
Round 4
Round 5
All others
Total

Answer 1

(a) MPC = 0.6

Multiplier = 1 / (1 - MPC)

=> Multiplier = 1 / (1 - 0.6)

=> Multiplier = 1 / 0.4

=> Multiplier = 2.5

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(b) MPC = 0.8

There is increase in investment spending by $9 billion.

	Change In income	Change in consumption	Change in saving
Round 1	$9 billion	0.8 * $9 billion = $7.2 billion	$1.8 billion
Round 2	$7.2 billion	0.8 * $7.2 billion = $5.76 billion	$1.44 billion
Round 3	$5.76 billion	0.8 * $5.76 billion = $4.608 billion	$1.152 billion
Round 4	$4.608 billion	0.8 * $4.608 billion = $3.6864 billion	$0.9216 billion
Round 5	$3.6854 billion	0.8 * $2.6854 billion = $2.94832 billion	$0.73708 billion
All others	$14.7466 billion	$11.79968 billion	$2.94692 billion
Total	$45 billion	$36 billion	$9 billion

In round 1, income will increase by the increase in investment.

Change in consumption in every round is the MPC multiply by the change in the income of that round.

Change in income of round 2 is equal to the change in consumption in round 1. Similarly, the change in income of round 3 is equal to the change in consumption in round 2 and so on.

Change in saving = Change in income - change in consumption.

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Multiplier = 1 / (1 - MPC)

=> Multiplier = 1 / (1 -0.8) => Multiplier = 1 / 0.2 => Multiplier = 5

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Multiplier = (change in income / change in investment )

=> 5 = Change in income / $9 billion

=> Change in income = 5 * $9 billion = $45 billion

Thus, the total change in income will be $45 billion.

and , MPC = Chnange in consumption / change in income

=> 0.8 = Change in consumption / $45 billion

=> Change in consumption = 0.8 * $45 billion

=> Change in consumption = $36 billion.

Thus, the total change in consumption will be $36 billion

Change in income till round 5 = $30.2534 billion

Change in income in all other rounds = ($45 - $30.2534) billion = $14.7466 billion

Change in consumption till round 5 = $24.20032 billion

Change in consumption in all other rounds = $36 billion - $24.20032 billion = $11.79968 billion.