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PROBLEM SET 1 - SOLUTIONS Due: April 11, 2001 (Wednesday) ECN - 105 Spring 2001 Instructions: Please complete you assignment in the space allotted. You must you show your work (albeit concisely). Reporting the answer alone will earn you no credit. This will allow the problem sets to be much more quickly and accurately graded. Chapter 2, Problem 6 (pp 38-39) a. Nominal GDP2000 = $ 10,000,000 Nominal GDP2010 = $ 15,200,000 Real GDP2010 = $ 10,000,000 Implicit Price Deflator2010 = 1.52 or 152 Consumer Price Index2010 = 1.60 or 160 b. How much have prices risen between 2000 and 2010? Laspeyres Index: prices have risen 60% Paasche Index: prices have risen 52% c. Advantages of CPI: A more focused measure of the consumer’s cost of living. Advantages of GDP deflator: Gives a more comprehensive view of the economy since it includes all goods and services. Conclusion: This answer can vary as it is not definitive. The student should mention the advantages and disadvantages of either measure. 1 Chapter 3, Problem 6, (pp 71-72) a. Sprivate = $ 750 Spublic = $ 0 S = $ 750 b. r = 5% c. Sprivate = $ 750 Spublic = $ - 250 S = $ 500 d. r = 10% 2 Working with Percentage Changes Economists often examine percentage changes in variables. The percentage change in real GDP from one year to the next, for example, represents economic growth during that year. The percentage change in the CPI or in the GDP deflator measure the rate of inflation for that year. The percentage change of the product of two variables is approximately equal to the sum of the percentage changes in each variable (the approximation is only valid for rather small percentage changes). Recall, nominal GDP = P Y where P is equal to the GDP deflator and Y is real GDP. Consequently, the percentage change in nominal GDP is approximately equal to the percentage change in P plus the percentage change in Y. Consider Table 2. Table 2 (1) Period 1 2 (2) Nominal GDP (PY) 100 105.06 (3) (4) % in PY P -1.00 5% 1.02 (5) % in P -2% (6) Y 100 103 (7) % in Y -3% a. Calculate the percentage changes in Y and P between periods 1 and 2 in Table 2 and complete columns (5) and (7). b. Using your answers in (5) and (7), calculate % change () in PY = _2_% + 3_% = __5_%. Place this number in column (3). c. Compute nominal GDP in period 2 exactly by calculating PY in period 2 = 1.02103 = 105.06. Therefore, the actual % in nominal GDP is equal to 100 (105.06 -100)/100=_5.06_%. d. If % in PY = % in P + % in Y, one can subtract % in Y from both sides to obtain: % in PY - % in Y = % in P. Recall that the GDP deflator = (Nominal GDP)/(Real GDP), or P = PY/Y. The % in a quotient is approximately equal to the % change in the numerator minus the % change in the denominator. Suppose you did not know the level of P in Table 2, but you knew the % in PY and Y in columns (3) and (7). You could then calculate % in P = % in PY - % in Y = __2_% e. As another example, consider labor productivity Y/L, which represents output per worker. Its percentage change from one year to the next is approximately equal to % change in Y plus/minus % change in L. Consequently, if Y grew by 5% in a year and L grew by 2%, the labor productivity would grow by approximately 3 or 7 % 3