Homework #1

1. How have total output and output per worker changes over time in the United States? How have these changes affected the lives of typical Americans?

1.     Both total output and output per worker have risen strongly over time in the United States. Output itself has grown by a factor of 100 in the last 133 years. Output per worker is now six times as great as it was in 1900. These changes have led to a much higher standard of living today.

2. Define budget deficit. Historically, when has the Federal government been most likely to run deficits? What has been the recent experience?

  2.   The budget deficit is the annual excess of government spending over tax collections. The U.S. federal government has been most likely to run deficits during wars. From the early 1980s to the mid-1990s, deficits were very large, even without a major war. The U.S. government ran surpluses for several years, from 1998 to 2001, but have run deficits since then.

3. Here are some macroeconomic data for the country of Oz for the years 1993 and 1994.

As the data suggests, Oz produces only potatoes, and its monetary unit is shekel. Calculate each of the following macroeconomic variables for Oz, being sure to give units.

a. Average labor productivity in 1993 and 1994.

b. The growth rate of average labor productivity between 1993 and 1994.

c. The employment rate in 1993 and 1994.

d. The inflation rate between 1993 and 1994.

1. (a)       Average labor productivity is output divided by employment:

      2009: 13,000 tons of potatoes divided by 900 workers = 14.44 tons of potatoes per worker

      2010: 14,300 tons of potatoes divided by 1100 workers = 13 tons of potatoes per worker

        (b)  The growth rate of average labor productivity is [(13-14.44/14.44)] ´ 100% = 10%.

        (c)  The unemployment and employment rates are:

2009: (100 unemployed/1000 workers) ´ 100% = 10% unemployed and 90% employed.

2010: (50 unemployed/1150 workers) ´ 100% = 4.3% unemployed and 95.7% employed.

        (d)  The inflation rate is [(2.8-2/2)/2 ] ´ 100% = 40%.

4. Prices were much higher in the United States in 1993 than in 1890. Does this fact mean that people were economically better off in 1890? Why or why not?

  4.   Just because prices were lower in 1890 than they were in 2009 does not mean that people were better off back then. People’s incomes have risen much faster than prices have risen over the last 100 years, so they are better off today in terms of real income.

5.  You are given the following data on an economy.

            Gross nation product                                       1000

            Governmental purchases of goods and services  200

            Governmental deficit                                            50

            National saving                                                  200

            Investment                                                         150

            Net factor payments from abroad                        25

GNP = GDP + NFP

Y = C + I + G + NX

S = S_pvt + Sgov

S= I + NX + NFP

S_pvt = PDI - C

Find the following:

a. Consumption = 600

b. Private saving = 250

c. Disposable income = 850

d. Gross domestic product = 975

e. Net Exports = 25

6. Consider an economy that produces three types of fruit: apples, oranges and bananas. In the base year, the production and price data were as follows.

In the current year the production and price data are as follows.

a. What are the values of nominal and real GDP in the base year and the current year?

b. How much did nominal GDP grow between the base year and the current year?

c. How much did real GDP grow between the base year and the current year?

d. What was the percentage change in the price level between base year and the current year, as measured by the GDP deflector?

(a)  Nominal GDP is just the dollar value of production in a year at prices in that year. Nominal GDP is $56 thousand in the base year and $200 thousand in the current year. Nominal GDP grew 257% between the base year and the current year: [($200,000/$56,000) - 1] ´ 100% = 257%.

(b)  Real GDP is calculated by finding the value of production in each year at base-year prices.
Thus, from the table above, real GDP is $56,000 in the base year and $178,000 in the current year. In percentage terms, real GDP increases from the base year to the current year by

[($178,000/$56,000) - 1] ´ 100% = 218%.

(c)  The GDP deflator is the ratio of nominal GDP to real GDP. In the base year, nominal GDP equals real GDP, so the GDP deflator is 1. In the current year, the GDP deflator is $200,000/$178,000 = 1.124. Thus the GDP deflator changes by [(1.124/1) - 1] ´ 100% = 12.4% from the base year to the current year.

(d)  Nominal GDP rose 257%, prices rose 12.4%, and real GDP rose 218%, so most of the increase
in nominal GDP is because of the increase in real output, not prices. Notice that the quantity of oranges quadrupled and the quantity of bananas more than doubled.

7. What is a production function? What are some factors that can cause a nation’s production function to shift over time? What do you have to know besides an economy’s production function to know how much output the economy can produce?

A production function shows how much output can be produced with a given amount of capital and labor. The production function can shift due to supply shocks, which affect overall productivity. Examples include changes in energy supplies, technological breakthroughs, and management practices. Besides knowing the production function, you must also know the quantities of capital and labor the economy has.

8. The production function slopes upward, but its slope declines from left to right. Give an economic interpretation of each of these properties of the production function.

The upward slope of the production function means that any additional inputs of capital or labor produce more output. The fact that the slope declines as we move from left to right illustrates the idea of diminishing marginal productivity. For a fixed amount of capital, additional workers each add less additional output as the number of workers increases. For a fixed number of workers, additional capital adds less additional output as the amount of capital increases.

9. The following data give real GDP,Y, Capital, K, and Labor, N, for the U.S. economy in various years.

Assume that the production function is Y=AK^0.3 N^0.7

a. How much did U.S. total factor productivity grow between 1960 and 1970? Between 1970 and 1980? Between 1980 and 1990?

b. What happened to the marginal product of labor between 1960 and 1990? Calculate the marginal product numerically as the extra output gained by adding 1 million workers in each of the two years.

(a)   To find the growth of total factor productivity, you must first calculate the value of A in the production function. This is given by A = Y/(K^.3N^.7). The growth rate of A can then be
calculated as

[(A_{year 2} - A_{year 1})/A_{year 1}] ´ 100%. The result is:

(b)  Calculate the marginal product of labor by seeing what happens to output when you add 1.0 to N; call this Y₂, and the original level of output Y₁. [A more precise method is to take the derivative of output with respect to N; dY/dN = 0.7A(K/N)^.3. The result is the same (rounded).]