**Hi Mr. Hartman,
Can you please demonstrate how chapter twelve (12) homework is done on the blog please? Your assistance will be greatly appreciated.
Thank you.
Natalia**

**Sure. Here are the questions. And the answers. I put how to do it nearby. **

**Natalia is the winner of 3 bonus points for finding the mistake in the answers to (e) below.**

Chapter 12

1. Given the data below on real GDP and potential GDP for the fictitious country “Alpha” determine each of the following:

a. the year-to-year growth rates of GDP

d. the output gap

e. the output gap as a percentage of potential GDP

f. whether the gap is expansionary or recessionary

## Year Real GDP Potential GDP

1990 17,500 17,300

(a) Can’t do: need two successive years.

(d) Y – Y* = 17500 – 17300 = 200: output gap is positive (real above potential), and this is an expansionary gap.

(e) 200/17500 = .01142 ≈ 1.14% is Output gap over real GDP. Question asks for output gap over potential GDP which is 200/17300 = .01156 ≈ 1.16%

1991 18,200 17,800

(a) 18200 – 17500 = 700; 700/17500 = 0.04 = 4%

(d) Y – Y* = 18200 – 17800 = 400: output gap is positive (real above potential), and this is an expansionary gap.

(e) 400/18200 = .02197 ≈ 2.2% is Output gap over real GDP. Question asks for output gap over potential GDP which is 200/17500 = .01142 ≈ 1.14%

1992 18,500 18,300

(a) 18500 – 18200 = 300; 300/18200 = .0164 ≈ 1.6% etc etc.

(d) Y – Y* = 18500 – 18300 = 200 etc. etc.

(e) 200/18500 = .0108 ≈ 1.08% is Output gap over real GDP. Question asks for output gap over potential GDP which is 200/18300 = .0109 ≈ 1.09% etc. etc.

1993 18,200 18,800

1994 18,600 19,300

1995 19,000 19,800

1996 19,400 20,800

1997 19,900 20,900

1998 20,600 21,100

1999 21,600 21,500

_______________________________________

2. Use the data in Problem 1 to graph the economic situation in “Alpha” during the 1990s. Label the phases of the business cycle on your graph.

Graph of output gaps in Alpha’s economy.

3. According to Okun’s Law, if a country’s output gap grows by 4%, its cyclical unemployment rate will grow by how much?

**2 percent. Okun’s law says half as much change in unemployment as in output gap. The output gap is considered negative. So a gap growing by 4% means things are getting worse by 4% so that the unemployment must be increasing by 2%.**

Answers:

Chapter 12

1a. year-to-year real GDP growth

1991 4.0%

1992 1.6%

1993 -1.6%

1994 2.2%

1995 2.2%

1996 2.1%

1997 2.6%

1998 3.5%

1999 4.9%

b. output gap

1990 200

1991 400

1992 200

1993 -600

1993 -700

1995 -800

1996 -1400

1997 -1000

1998 -500

1999 100

c. output gap as a percent of GDP.

**Put gap above in (a) over the real GDP to get these figures. Question asks for Output gap over Potential GDP, so all these are a bit wrong. See above for calculations. Thanks to Natalia Verance for finding this error.**

1990 1.14

1991 2.19

1992 1.08

1993 3.29

1994 3.76

1995 4.21

1996 7.21

1997 5.03

1998 2.43

1999 0.46

d. is the gap recessionary or expansionary? **Positive numbers above in (a) are expansionary; when Y > Y*.**

1990 E

1991 E

1992 E

1993 R

1994 R

1995 R

1996 R

1997 R

1998 R

1999 E

** **

3. 2% Obvious. 2% change in unemployment x 2 = makes 4% change in GDP; but output gap goes up 4% implies unemployment goes down 2%