Economics 115 Homework #1: Answers. Table 1. Year GDP GDP CPI 2008 $3,055 $3, $3,170 $3, $3,410 $3,

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1 Economics 115 Homework #1: Answers Table 1 Nominal Real Year GDP GDP CPI 2008 $3,055 $3, $3,170 $3, $3,410 $3, $3,780 $3, Complete Table 1. Show your work. ($3,055/94)100 = x = $3,250 $3,170 = (x/100)100, x = $3,170 $3,280 = ($3,410/x)100, x = ($3,410/$3,280)100 = 104 $3,500 = (x/108)100, x = $3,780

2 2. Assume Nominal GDP doubles between year 1 and year 2. a. If the average level of prices doubles between year 1 and year 2, what has happened to Real GDP? Nominal GDP in Year 1 = X1, CPI1 = 100 Nominal GDP in Year 2 = 2X1, CPI2 = 200 Real GDP1 = (X1/100)100 and Real GDP2 = (2X1/200)100 So: Real GDP1 = Real GDP2 (No change in Real GDP) b. If the average level of prices has less than doubled between year 1 and year 2 what has happened to Real GDP? CPI1 = 100 and CPI2 = 150 Real GDP1 = (X1/100)100 and Real GDP2 = (2X1/150)100 or X1(4/3) So Real GDP2 > Real GDP1 (Real GDP has risen) c. If the average level of prices has more than doubled between year 1 and year 2, what has happened to Real GDP? CPI1 = 100 and CPI2 = 250 Real GDP1 = (X1/100)100 and Real GDP2 = (2X1/250)100 or X1(4/5) So Real GDP2 < Real GDP1 (Real GDP has fallen)

3 3. Given the data below, answer the following: May 2010: NILF = 100m, E = 110m, U = 10m. a. If 5m teenagers (16 years or over) enter the labor force (LF) in June 2010 ( LF = 5m) and 4m find employment ( E = 4m), calculate the uer for May and June. LF = 5m = E + U = 4m + 1m May: uer = U/(U + E) = 10m/(10m + 110m) = = 8.3% June: uer = U/(U + E) = 11m/(11m + 114m) = = 8.8% b. Calculate the labor force (LF) and those not in labor force (NILF) for June. May: LF = 110m + 10m = 120m June: LF = 114m + 11m = 125m; NILF = 100m - 5m = 95m c. Start with the data from May Suppose instead that 3m unemployed workers drop out of the labor force in June ( U = -3m). Calculate U, E, LF and NILF and uer. May: uer = U/(U + E) = 10m/(10m + 110m) = 8.3% NILF = 100m, E = 110m, U = 10m, LF = 110m + 10m June: NILF = 103m, U = 7m, E = 110m, LF = 110m + 7m uer = 7m/(110m + 7m) = 7m/117m = 6.0%

4 4. When the rate of inflation is expected to be zero, Larry wants to lend money if the interest rate is at least 5% while Moe wants to borrow money if the interest rate is 5% or less. Thus they make a loan agreement at 5% when inflation is expected to be zero. a. If they both expect inflation of 4% over the period of the loan, what interest rate will they agree to? 9%, since the 4% expected inflation rate must be added to the 5% interest rate (keeps purchasing power of principal plus interest constant) b. If they both expect deflation of 2% over the period of the loan, what interest rate will they agree to? 3%, since the 2% expected deflation rate must be subtracted from the 5% interest rate (same reason) c. Suppose Larry expects the rate of inflation to be 4% but Moe expects it to be 6%. Will they be able to work out a loan agreement? If so, at what rate of interest? Larry is willing to lend money at 9% or more Moe is willing to borrow money at 11% or less They can agree on any interest rate between 9% and 11% (including 9 and 11% but probably at 10%)

5 5. Workers at IBM have worked out a wage agreement under the expectation that the rate of inflation will be zero over the period of the contract. In order, to protect the workers against unanticipated inflation, however, the contract is indexed. This means that at the end of each year the nominal wage rate will increase by the same percentage as the Consumer Index (CPI). At the beginning of the contract period the CPI is 214 and the nominal wage rate is $10 an hour. At the end of the first year the CPI is 225 and at the end of the second year the CPI is 234. Nominal Real Year CPI Wage Wage $10/Hr $4.67/Hr x1 $4.67/Hr x2 $4.67/Hr ($10/214)100 = $4.67 = Real wage Basic idea: Want to keep real wage constant (Assumes no increase in the real wage) a. What will the new nominal wage rate be at the end of the first year? Real Wage = $4.67/Hr (x1/225)100 = $4.67/Hr x1 = $4.67(225/100) x1 = $4.67(2.25)/Hr = $10.51/Hr b. What will the new nominal wage rate be at the end of the second year? Real Wage = $4.67/Hr (x2/234)100 = $4.67/Hr x2 = $4.67(234/100) x2 = $4.67(2.34)/Hr = $10.93/Hr

6 6. Calculate the following: a. If the price index in year 1 is 100 and the inflation rate is 8% for each of the next 3 years, what is the price index for each of these 3 years? Show your work % % % Year 2: P = P(1+p) = 100.0(1.08) = 108 Year 3: P = 108.0(1.08) = 100.0(1.08) 2 = Year 4: P = 116.6(1.08) = 100.0(1.08) 3 = Note: p = ΔP/P b. If the price index in year 1 is 100 and the inflation rate is 7%, 8% and 9% in each of the next 3 years, what is the price index for each of these 3 years? Show your work % % % Year 2: P = P(1+p) = 100.0(1.07) = 107 Year 3: P = 107.0(1.08) = 100.0(1.07)(1.08) = Year 4: P = 115.6(1.09) = 100.0(1.07)(1.08)(1.09) = 126.0

7 c. If the price index is 200 in year 1 and the inflation rate is 10%, 8%, and 6% for each of the next 3 years, what is the price index for each of these 3 years? Show your work % % % Year 2: P = P(1+p) = 200(1.1) = 220 Year 3: P = 220(1.08) = 200(1.1)(1.08) = Year 4: P = 237.6(1.06) = 220(1.08)(1.06) = 200(1.1)(1.08)(1.06) = d. If the price index for year 1 is 200 and the deflation rate is 8% a year for each of the next 3 years, what is the price index for each of these 3 years? Show your work % % % Year 2: P = P(1-p) = 200.0(0.92) = 184 Year 3: P = 184.0(0.92) = 200.0(0.92) 2 = 200.0(0.8464) = Year 4: P = (0.92) = 200.0(0.92) 3 = 200.0(0.7787) =

8 e. If the price index for year 1 is 100 and the deflation rate is 8%, 7%, and 6% for the next 3 years, what is the price index for each of these 3 years? Show your work % % % Year 2: P = 100.0(1-0.08) = 92.0 Year 3: P = 92.0(1-0.07) = 100(1-0.08)(1-0.07) = Year 4: P = 85.56(1-0.06) = 100.0(1-0.08)(1-0.07)(1-0.06) = 80.43