Worked Problems
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Problem 16.1 - Equilibrium GDP
Problem:
Suppose a private closed economy's consumption schedule is given by the following:
GDP=DI / C / I
6600 / 6680 / 80
6800 / 6840 / 80
7000 / 700 / 80
7200 / 7160 / 80
7400 / 7320 / 80
7600 / 7480 / 80
7800 / 7640 / 80
8000 / 7800 / 80
Use the values in the table to answer the following:
  1. If planned investment is R80 and independent of output, what is the equilibrium level of GDP?
  2. What is the level of saving at the equilibrium level of GDP?
  3. Suppose GDP is R7600. 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 R7400. R7320 + R80 = R7400.
  2. Saving is the difference between disposable income and consumption. When GDP = DI = R7400, saving is R80. 80 = R7400 - 7320.
  3. The unplanned inventory adjustment is the difference between what is produced and what is purchased, either as consumption or planned investment. At a GDP of R7600, planned expenditures are R7480 + R80 = R7560. The unplanned inventory adjustment is then R40 = R7600 - R7560. This unplanned increase in inventories will likely lead firms to produce less output in the future.

Problem 16.2 - Complete aggregate expenditures model
Problem:
Suppose a private closed economy has an MPC of .8 and a current equilibrium GDP of R7400 billion.
  1. What is the multiplier in this economy?
  2. Now suppose the economy opens up trade with the rest of the world and adds net exports of R20 billion. What impact will this have on equilibrium real GDP?
  3. Suppose the government plans to spend R100 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 R100 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 R100 billion. R100 = 5 x R20. Real GDP rises from R7400 to R7500 billion.
  3. GDP will increase by the multiplier times the initial amount of government spending, or R500 billion in this instance. R500 = 5 x R100.
  4. A lump-sum tax of R100 billion reduces disposable income by R100 billion at every level of real GDP. Since the MPC is .8, consumption will initially fall by R80 billion. Multiplied by the multiplier of 5, this translates to a drop in GDP of R400. R400 = 5 x R80.

Problem 16.3 - Expenditure gaps
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:
Employment / Real GDP / Aggregate Expenditure
100 / 1200 / 1275
105 / 1300 / 1350
110 / 1400 / 1425
115 / 1500 / 1500
120 / 1600 / 1575
125 / 1700 / 1650
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. If the economy was at equilibrium R200 billion below its potential, what is the size of the recessionary expenditure gap?
/ Answer:
  1. Equilibrium GDP is R1500 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 R1500 billion while full employment GDP is R1600 billion. The gap is the difference between real GDP and aggregate expenditures at the full employment level, or R25 billion (+ R1600 - R1575.) Said differently, if expenditures were to increase by R25 at each level of real GDP, real GDP and aggregate expenditures would be equal at full employment.
  3. Aggregate expenditures rise by R75 billion for each R100 billion in real GDP, so the MPC is .75. The multiplier is 4. 1/(1- .75) = 4.
  4. With a multiplier of 4, an additional expenditure of R50 billion is required to return to full employment. R50 = R200/4.