PROBLEMS

  1. Question 13.1

    An economy has a marginal propensity to consume of 0.6, real GDP equals $500 billion, and the government collects 20% of GDP in taxes. If government purchases increase by $10 billion, show the rounds of increased spending that take place by completing the accompanying table. The first and second rows are filled in for you. In the first row, the increase in government purchases of $10 billion raises real GDP by $10 billion, taxes increase by $2 billion, and YD increases by $8 billion; in the second row, the increase in YD of $8 billion increases consumer spending by $4.80 billion (MPC × change in disposable income).

     

    Change in G or C

    Change in real GDP

    Change in taxes

    Change in YD

    Rounds

     

    (billions of dollars)

     

     1

    ΔG = $10.00

    $10.00

    $2.00

    $8.00

     2

    ΔC =   4.80

    4.80

    0.96

     3.84

     3

    ΔC =   ?

    ?

    ?

    ?

     4

    ΔC =   ?

    ?

    ?

    ?

     5

    ΔC =   ?

    ?

    ?

    ?

     6

    ΔC =   ?

    ?

    ?

    ?

     7

    ΔC =   ?

    ?

    ?

    ?

     8

    ΔC =   ?

    ?

    ?

    ?

     9

    ΔC =   ?

    ?

    ?

    ?

    10

    ΔC =   ?

    ?

    ?

    ?

    1. What is the total change in real GDP after the 10 rounds? What is the value of the multiplier? What would you expect the total change in real GDP to be, based on the multiplier formula? How do your two answers compare?

    2. Redo the accompanying table, assuming the marginal propensity to consume is 0.75 and the government collects 10% of the rise in real GDP in taxes. What is the total change in real GDP after 10 rounds? What is the value of the multiplier? How do your two answers compare?

WORK IT OUT

For interactive, step-by-step help solving the following problem, check out this Work It Out tutorial under student resources.

Question 13.2

2. Calculate the change in government purchases of goods and services necessary to close the recessionary or inflationary gaps in the following cases. Assume that the short-run aggregate supply curve is horizontal, so that the change in real GDP arising from a shift of the aggregate demand curve equals the size of the shift of the curve.

  1. Real GDP equals $100 billion, potential output equals $160 billion, the government collects 20% of any change in real GDP in the form of taxes, and the marginal propensity to consume is 0.75.

  2. Real GDP equals $250 billion, potential output equals $200 billion, the government collects 10% of any change in real GDP in the form of taxes, and the marginal propensity to consume is 0.5.

  3. Real GDP equals $180 billion, potential output equals $100 billion, the government collects 25% of any change in real GDP in the form of taxes, and the marginal propensity to consume is 0.8.