Chapter 1. Section 7(19), Problem 9

Step 1

Work It Out
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You must read each slide, and complete any questions on the slide, in sequence.

Question

The accompanying table shows gross domestic product (GDP), disposable income (YD), consumer spending (C), and planned investment spending (IPlanned) in an economy. Assume there is no government or foreign sector in this economy.

Complete the table by calculating planned aggregate spending (AEPlanned) and unplanned inventory investment (IUnplanned).

GDP YD C IPlanned AEPlanned IUnplanned
(billions of dollars)
$0 $0 $100 $300 $oB+yi+WLu7/s/QRSAYX7X+97z/HdAR/4 $lhwTLaU5s+C9R1v6k6FNRhnuM0UnvuRD
400 400 400 300 kBG56QeT2Fk2g7WmNsO5bh+16Mw10ZcU byC3O7PRMgKhIDqCAqxFQa4PB60VaruJ
800 800 700 300 tCiEr0SqMjxdHsmtqoxESZulhuy5QDir g5AmdmtEVa28n9x4w051sigeJ50U4Me8
1,200 1,200 1,000 300 tYhgO3MjZ9RBSXRb6HKstGsc6OsSOYwv ft7rDVi7z3nxS/8oxXCPxwHEPtSeRhvc
1,600 1,600 1,300 300 VZaETiaExu3qNSwsC+t5bEQcDfZuglP/ U/NDibDUa4rbNsKaO+TeLaEvr2qjFc7u
2,000 2,000 1,600 300 3R0jOX4ATrckheK29Q8E7crp8r2i0Z1Z PIVhbbGR6WiuCKnR8fV2rE2dqVJc9S91
2,400 2,400 1,900 300 Hq0UjpxrUjs/IvlR5O0Q1RfgzDwYULf/ PiLcTTUonjWoVWGoAzrAhdu4k0cMmZTS
2,800 2,800 2,200 300 k19/2eC7QDSMbMoF1aFtikLw/+yJrJ1F RE85bQwTIzcT+1JFic6bATxECz6w5yfs
3,200 3,200 2,500 300 vHLGH99IqX2mrcEd7MRi/3JvCIJxzhz2 JpQT4eusK6V1htGYFCbxP/DlT4eaZ2hs
Table
AEPlanned is the sum of consumption and Iplanned. So when C is $100 and Iplanned is $300 then AEPlanned is $400. The remaining values of AEPlanned are found by adding C and Iplanned for all levels of GDP. You can find IUnplanned as the difference between disposable income and AEplanned. When GDP is $0, IUnplanned is -$400 ($0 - $400). You can find the remaining values of IUnplanned by taking the difference in GDP and AEplanned for all values of GDP. For further review see section “Inventories and Unplanned Investment Spending.”
Complete the table by calculating planned aggregate spending (AEPlanned) and unplanned inventory investment (IUnplanned).
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Step 2

Question

Using the table below what is the aggregate consumption function?

GDP YD C IPlanned AEPlanned IUnplanned
(billions of dollars)
$0 $0 $100 $300 $400 -$400
400 400 400 300 700 -300
800 800 700 300 1000 -200
1,200 1,200 1,000 300 1300 -100
1,600 1,600 1,300 300 1600 0
2,000 2,000 1,600 300 1900 100
2,400 2,400 1,900 300 2200 200
2,800 2,800 2,200 300 2500 300
3,200 3,200 2,500 300 2800 400
Table

The consumption function can be written as: C = $b0g0iQ1whKk= billion + vYXgcddeLXk=YD

We can find the aggregate consumption function by calculating aggregate autonomous consumer spending and the marginal propensity to consume. Aggregate autonomous consumer spending equals aggregate consumer spending when disposable income is zero; in this case, aggregate autonomous consumer spending is $100 billion. The marginal propensity to consume is the change in aggregate consumer spending divided by the change in disposable income; in this case, it is 0.75 [= ($400 − $100)/($400 − $0)]. For further review see section, “Consumer Spending.”
The consumption function can be written as: C = ______ billion + ______YD
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Step 3

Question

Using the table below, what is Y*, income-expenditure equilibrium GDP?

GDP YD C IPlanned AEPlanned IUnplanned
(billions of dollars)
$0 $0 $100 $300 $400 -$400
400 400 400 300 700 -300
800 800 700 300 1000 -200
1,200 1,200 1,000 300 1300 -100
1,600 1,600 1,300 300 1600 0
2,000 2,000 1,600 300 1900 100
2,400 2,400 1,900 300 2200 200
2,800 2,800 2,200 300 2500 300
3,200 3,200 2,500 300 2800 400
Table
Iso2X3cOqhRs4QvteL4DD0XAW3OC+1FvI0kvhvi8SD8D5IimbksOYdjRy+QloFnTw7EW5QMdLHgFCbnf4I5OabgiCChmeJZDCUtgWexZfT2Dw9phUDg1pa7MTeIxMOXnhbPQGLmo9gGINIVjKtiTWyJMn6Y3SdUnsSA1cgbexofnHN+68AgxSB9MxeugjMmqGqhN/HWLXSmMijjBXwsGwcyb1uganmW8EkYxmEq9BCfr7ml8LmjkrWfJvmSyl/Ysp4Ivv4MHQnY4Q21T/EU0gHANMyMzv8k0SenelctsHPXhK7xakED5Bl37p77QsWUdNfB2clR4m+s=
Correct! For further review see section, “The Income-Expenditure Multiplier.”
Incorrect. Y* is the level of GDP at which planned aggregate spending equals GDP. From the accompanying table, Y* is $1,600 billion. For further review see section, “The Income-Expenditure Multiplier.”
Using the table below, what is Y*, income-expenditure equilibrium GDP?
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Step 4

Question

Recall the consumption function is C = $100 billion + 0.75 x YD and the original equilibrium value of Y* is $1,600 billion. Use the table below to answer each of the following

GDP YD C IPlanned AEPlanned IUnplanned
(billions of dollars)
$0 $0 $100 $300 $400 -$400
400 400 400 300 700 -300
800 800 700 300 1000 -200
1,200 1,200 1,000 300 1300 -100
1,600 1,600 1,300 300 1600 0
2,000 2,000 1,600 300 1900 100
2,400 2,400 1,900 300 2200 200
2,800 2,800 2,200 300 2500 300
3,200 3,200 2,500 300 2800 400
Table

What is the value of the multiplier?

The multiplier is h4XZagboIgc=.

Recall the multiplier equals 1/(1 − MPC); the value of the multiplier is 4 = 1/(1 − 0.75). For further review see section, “The Income-Expenditure Multiplier.”
What is the value of the multiplier?

Question

If planned investment spending falls to $200 billion, what will be the new Y*?

The new equilibrium level of GDP is $WYWjVQzT4dmH8TewByKWKg== billion.

Correct! For further review see section, "The Income-Expenditure Multiplier."
Sorry, planned investment spending will decrease by $100 billion to $200 billion, the new Y* will equal $1,200 billion. If planned investment spending equals $200 billion, it has fallen by $100 billion. Since the multiplier is 4, Y* will change by four times the change in planned investment spending, or decrease by $400 billion. For further review see section, “The Income-Expenditure Multiplier.”
If planned investment spending falls to $200 billion, what will be the new Y*?

Question

If autonomous consumer spending rises to $200 billion, what will be the new Y*?

The new equilibrium level of GDP is $W9ZYWUD5NT8aLa3R8qnWDQ== billion.

If autonomous consumer spending rises to $200 billion from $100 billion, the new Y* will equal $2,000 billion. If autonomous consumer spending equals $200 billion, it has risen by $100 billion. Since the multiplier is 4, Y* will change by four times the change in autonomous consumer spending, or increase by $400 billion.For further review see section, “The Income-Expenditure Multiplier.”
If autonomous consumer spending rises to $200 billion, what will be the new Y*?
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