Problem:

The consumption and investment schedules for a private closed economy are given in the following table:

Use the values in the table to answer the following:

1. What is the equilibrium level of GDP?
2. What is the level of saving at the equilibrium level of GDP?
3. Suppose actual GDP is $7600. How much unplanned inventory change will occur? What will likely happen to GDP as a result?

Answer:

1. Equilibrium GDP occurs where the level of planned expenditures—consumption and planned investment in a private closed economy—equals the level of GDP. In this example, equilibrium occurs at a GDP of $7400. $7320 + $80 = $7400.
2. Saving is the difference between disposable income and consumption. When GDP = DI = $7400, saving is $80. 80 = $7400 – 7320.
3. The unplanned inventory adjustment is the difference between what is produced and what is purchased, whether purchased as consumption or as planned investment. If a GDP of $7600 is produced, consumers would plan to spend $7480 and planned investment spending is $80, for a combined total of $7560. The unplanned inventory adjustment is then $7600 – $7560 = $40. This unplanned increase in inventories will likely lead firms to produce less output in the future.

Problem:

Suppose a private closed economy has an MPC of .8 and a current equilibrium GDP of $7400 billion.

1. What is the multiplier in this economy?
2. Now suppose the economy opens up trade with the rest of the world and experiences net exports of $20 billion. What impact will this have on equilibrium real GDP?
3. Next suppose a government is introduced, and plans to spend $100 billion. By how much will this change in spending ultimately cause GDP to change, and in what direction?
4. In order to finance this expansion of government spending, suppose the government decides to levy a lump-sum tax of $100 billion. By how much will GDP change, and in what direction?

Answer:

1. The multiplier is 1/(1 – .8) = 5.
2. These positive net exports represent an initial increase in spending. The increase in GDP will be the multiplier times this initial injection, or $100 billion. 5 x $20 = $100. Real GDP rises from $7400 to $7500 billion.
3. GDP will increase by the multiplier times the initial amount of government spending: 5 x $100 = $500.
4. A lump-sum tax of $100 billion reduces disposable income by $100 billion at every level of real GDP. Since the MPC is .8, consumption will initially fall by $80 billion. Multiplied by the multiplier of 5, this translates to a drop in GDP of 5 x $80 = $400.

Problem:

Suppose an economy can be represented by the following table, in which employment is in millions of workers and GDP and AE are expressed in billions of dollars:

Use the table to answer the following:

1. What is the equilibrium level of GDP?
2. What kind of expenditure gap exists if full employment is 120 million workers? What is its size?
3. Suppose government spending, taxes, and net exports are all independent of the level of real GDP. What is the multiplier in this economy?
4. Suppose instead that the economy is producing at equilibrium GDP. If this GDP is $200 billion below the economy's potential, what is the size of the recessionary expenditure gap?

Answer:

1. Equilibrium GDP is $1500 billion, the level at which real GDP equals aggregate expenditures.
2. Equilibrium employment is 115, so the economy is suffering a recessionary expenditure gap: equilibrium GDP is $1500 billion while full employment GDP is $1600 billion. The gap is the difference between real GDP and aggregate expenditures at the full employment level, or $25 billion (= $1600 – $1575.) Said differently, if expenditures were to increase by $25 at each level of real GDP, real GDP and aggregate expenditures would be equal at full employment.
3. Aggregate expenditures rise by $75 billion for each $100 billion in real GDP, so the MPC is .75. The multiplier is 1/(1– .75) = 4.
4. With a multiplier of 4, an additional expenditure of $50 billion is required to return to full employment. $50 = $200/4.