Chapter 2 national income accounting

Technical Problems

1.    The text calculates the change in real GDP in 1996 prices in the following way:

        [RGDP04 -  RGDP96]/RGDP96 = [3.50 - 1.50]/1.50 = 1.33 = 133%.

    To calculate the change in real GDP in 2004 prices, we first have to calculate the GDP of 1996 in 2004 prices. Thus we take the quantities consumed in 1996 and multiply them by the prices of 2004, as follows:

                                   Beer         1 at $2.00 =  $2.00
        Skittles       1 at $0.75 =  $0.75
                                              _______________________________
                                  Total                     $2.75

    The change in real GDP can now be calculated as  [6.25 - 2.75]/2.75 = 1.27 = 127%.

    We can see that the growth rate of real GDP calculated this way is roughly the same as the growth rate calculated above.

2.a.    The relationship between private domestic saving, private domestic investment, the budget deficit, and net exports is shown by the following identity:
 
                S - I  (G + TR - TA) + NX.

    Therefore, if we assume that transfer payments (TR) remain constant, an increase in taxes (TA) has to be offset either by an increase in government purchases (G), an increase in net exports (NX), or a decrease in the difference between private domestic saving (S) and private domestic investment (I).

2.b.     From the equation YD  C + S it follows that an increase in disposable income (YD) will be reflected in an increase in consumption (C), saving (S), or both.

2.c.     From the equation YD  C + S it follows that when either consumption (C) or saving (S) increases, disposable income (YD) must increase as well.

3.a.      Since depreciation is defined as D = Ig - In = 800 - 200 = 600  ==> 

        NDP = GDP - D = 6,000 - 600 = 5,400.

3.b.     From GDP = C + Ig + G + NX  ==>  NX = GDP - C – Ig - G  ==>

        NX = 6,000 - 4,000 - 800 - 1,100 = 100.

3.c.     BS = TA - G - TR   ==> (TA - TR) = BS + G ==> (TA - TR) = 30 + 1,100 = 1,130
 
3.d.     YD = Y - (TA - TR) = 6,000 - 1,130 = 4,870

3.e.      S = YD - C = 4,870 - 4,000 = 870

4.a.      S = YD - C = 5,100 - 3,800 = 1,300

4.b.     From S - I = (G + TR - TA) + NX  ==> I = S - (G + TR - TA) - NX = 1,300 - 200 - (-100) = 1,200.

4.c.     From Y = C + I + G + NX ==> G = Y - C - I - NX ==>

              G = 6,000 - 3,800 - 1,200 - (-100) = 1,100.

      Also: YD = Y - TA + TR ==> TA - TR = Y - YD = 6,000 - 5,100 ==> TA - TR = 900

      From BS = TA - TR - G ==> G = (TA - TR) - BS = 900 - (-200) ==>   G = 1,100.

5.    According to Equation (2) in the text, the value of total output (in billions of dollars) can be calculated as: Y = labor payments + capital payments + profits = $6 + $2 + $0 = $8.

6.a.    Since nominal GDP is defined as the market value of all final goods and services currently produced in this country, we can only measure the value of the final product (bread), and therefore we get $2 million (since 1 million loaves are sold at $2 each).

6.b.     An alternative way of measuring GDP is to calculate all the value added at each step of production. The total value of the ingredients used by the bakeries can be calculated as:

       1,200,000 pounds of flour ($1 per pound)        =  1,200,000
             100,000 pounds of yeast ($1 per pound)        =     100,000
             100,000 pounds of sugar ($1 per pound)        =     100,000
             100,000 pounds of salt    ($1 per pound)        =     100,000
       __________________________________________________________
                                                                                            = 1,500,000

Since $2,000,000 worth of bread is sold, the total value added at the bakeries is $500,000.
 
7.       If the CPI increases from 2.1 to 2.3, the rate of inflation can be calculated in the following way:

rate of inflation = (2.3 - 2.1)/2.1 = 0.095 = 9.5%.

The CPI often overstates inflation, since it is calculated by using a fixed market basket of goods and services. But the fixed weights in the CPI's market basket cannot capture the tendency of consumers to substitute away from goods whose relative prices have increased. Quality improvements in goods also often are not adequately taken into account. Therefore, the CPI will overstate the increase in consumers' expenditures.

8.    The real interest rate (r) is defined as the nominal interest rate (i) minus the rate of inflation (). Therefore the nominal interest rate is the real interest rate plus the rate of inflation, or

        i = r +  = 3% + 4% = 7%.
 

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