Econ 1 - Problem Set 7 With Solutions

Problem Set 7 Hard copies of your answers are due at the beginning of your section, either on Thursday, November 10, or Friday, November 11. For example, if your section starts at 10:00am on Friday, you should submit your answers to your TA in your section classroom at 10:00am on Friday, November 11. Late problems earn zero points. Note: you can work on these problems or your own, or in a small group with other current Econ 1 students. If you choose to work in a group, each student needs to hand in a separate, individual copy to his/her TA. 1. Taylor, chapter 18, problem 7 2. Taylor, chapter 18, problem 10 Note: Taylor, fourth edition

Question 1 (Chapter 18, Problem 7) (a)

We calculate nominal GDP for 2001 by multiplying the value and the quantity for each good and then summing over the goods: ($2.50 x 1,000) + ($1.25 x 500) + ($100.00 x 10) = $2,500 + $625 + $1,000 = $4,125. We calculate nominal GDP for 2002 in the same way: ($3.50 x 800) + ($2.25 x 400) + ($100.00 x 14) = $2,800 + $900 + $1,400 = $5,100.

(b)

Using 2001 prices: 2001 GDP is $4,125 as shown in part (a). 2002 GDP is ($2.50 x 800) + ($1.25 x 400) + ($100.00 x 14) = $2,000 + $500 + $1,400 = $3,900. The difference is $3,900 – $4,125 = – $225. The percentage change in GDP is – $225 divided by $4,125 which is equal to –.0545 or – 5.45%. Using 2002 prices: 2001 GDP is ($3.50 x 1,000) + ($2.25 x 500) + ($100.00 x 10) = $3,500 + $1,125 + $1,000 = $5,625. 2002 GDP is $5,100 as shown in part (a). The difference is $5,100 – $5,625 = – $525. The percentage change in GDP is – $525 divided by $5,625 which is equal to –.0933 or – 9.33%.

(c)

The percentage change in GDP is slightly different depending on whether 2001 or 2002 prices are used. “Such differences are inevitable, because there is no reason to prefer the prices in one year to those of another year when controlling for inflation. Economists arrive at a single percentage by simply averaging the two percentages” (Taylor, p. 469). Here we have a 5.45% decrease in GDP if we use 2001 prices and a 9.33 % decrease if we use 2002 prices. To average, we add 5.45 and 9.33 and then divide by 2. This gives us that the percent change in real GDP is equal to – 7.39%. A geometric average can be used. The geometric average is the square root of the product of the two numbers: (0.0545 × 0.0933) = 7.13 . Therefore, using a geometric average, the percent change in real GDP is equal to – 7.13%. Either answer is acceptable.

(d)

In part (a) we found that 2002 nominal GDP is $5,100. We are given that 2001 is the base year, so we can find 2002 real GDP using 2001 prices and 2002 quantities. From part (b) we found 2002 real GDP using 2001 prices to be $3,900. The 2002 deflator is found by dividing 2002 nominal GDP by $5,100 2002 real GDP: = 1.31 $3,900 Alternate Answer 1: We are given that the GDP deflator for 2001 is equal to 1.0. This means that 2001 nominal GDP is equal to 2001 real GDP. In (c) we

found that real GDP declined by 7.39 % (using a simple average). Therefore, 2002 real GDP is equal to (1-.0739) x $4,125 = $3,820. The 2002 deflator is $5,100 = 1.34 found by dividing 2002 nominal GDP by 2002 real GDP: $3,820

Alternate Answer 2: We are given that the GDP deflator for 2001 is equal to 1.0. This means that 2001 nominal GDP is equal to 2001 real GDP. In (c) we found that real GDP declined by 7.13 % (using a geometric average). Therefore, 2002 real GDP is equal to (1-.0713) x $4,125 = $3,820. The 2002 deflator is found by dividing 2002 nominal GDP by 2002 real GDP: $5,100 = 1.33 $3,830

Question 2 (Chapter 18, Problem 10) a) –$5 billion: Inventory investment = change in inventory stock = 5 – 10 = –5 b) $4 billion: Net exports (X) = exports – imports = 21 – 17 = 4 c) $231 billion: GDP = Consumption (C) + Investment (I) + Government expenditures (G) + Net exports (X) = 140 + (27 – 5) + 65 + 4 = 231 d) –$10 billion: Statistical discrepancy = (C+I+G+X) – (labor income + capital income + depreciation + indirect business taxes + net income of foreigners) = 231 – (126 + 70 + 12 + 28 + 5) = 231 – 241 = –10 e) $26 billion: National savings = GDP – C – G = 231 – 140 – 65 National Saving = 26 Investment + Net Exports = I + X = (27– 5) + 4 = 26