Chapter 6. Chapter 6

Work It Out
Chapter 6
true
true

The United States, Japan, and China are among the world’s largest producers. To answer the following questions, assume that their markets are monopolistically competitive and use the gravity equation [MATH: B = 93 ](constant B is equal to 93) and [MATH: n = 1.25 ](the distance, n, is equal to 1.25) .

GDP in 2015 ($ Billions) Distance from the United States (miles)
China 11,385 7,245
Japan 4,116 6,314
United States 17,968 -

Question 6.1


a. Using the gravity equation, compare the expected level of trade between the United States and Japan and between the United States and China.

Hint: Round your numbers to two decimal places.

United States and Japan: $55C2gMaaNw8EYt0bq5dbPUNPsMnFC6UafHse4XY+LM7blIGoZonRn6HO84NkKJefEUvgh+bn1APTbZpazgeHcA== billion

United States and China: $o0NPNYuUh6XSw90VY1eFRNqmK0WV0ceNPJC5AhKcvEfaUESyvrQ8/cytY7LovKDCYjVoqB8uFCMuzCEIwVWX+Q== billion
Correct. The expected level of trade between the United States and Japan is calculated using the gravity equation [MATH: \text{Trade}=\frac{B\cdot{GDP_1}\cdot{GDP_2}}{\text{dist}^n} ](trade equals the expected level of trade is equal to B multiplied by gross domestic product of country 1 multiplied by the gross domestic product of country 2, divided by the distance between the two countries raised to a power n ) . Solving yields [MATH: \frac{93\cdot{4,116}\cdot{17,968}}{{6,314}^{1.25}}=\$122,201.72 ](equal 93 multiplied by the value of the gravity term, which is 4,116 for Japan times 17,968 for United States divided by the distance between the United States and Japan which is 6,314 raised to the 1.25 power equal to $122,201.72 billion.) billion. The expected level of trade between the United States and China is calculated using the gravity equation as [MATH: \frac{93\cdot{11,385}\cdot{17,968}}{{7,245}^{1.25}}=\$284,621.51 ](equal 93 multiplied by the value of the gravity term, which is the 11,385 for China times the 17,968 for United States, divided by the distance between the United States and China which is 7,245 raised to the 1.25 power equal to $284,621.51 billion.) billion.
Incorrect. The expected level of trade between the United States and Japan is calculated using the gravity equation [MATH: \text{Trade}=\frac{B\cdot{GDP_1}\cdot{GDP_2}}{\text{dist}^n} ](trade equals the expected level of trade is equal to B multiplied by gross domestic product of country 1 multiplied by the gross domestic product of country 2, divided by the distance between the two countries raised to a power n ) . Solving yields [MATH: \frac{93\cdot{4,116}\cdot{17,968}}{{6,314}^{1.25}}=\$122,201.72 ](equal 93 multiplied by the value of the gravity term, which is 4,116 for Japan times 17,968 for United States divided by the distance between the United States and Japan which is 6,314 raised to the 1.25 power equal to $122,201.72 billion.) billion. The expected level of trade between the United States and China is calculated using the gravity equation as [MATH: \frac{93\cdot{11,385}\cdot{17,968}}{{7,245}^{1.25}}=\$284,621.51 ](equal 93 multiplied by the value of the gravity term, which is the 11,385 for China times the 17,968 for United States, divided by the distance between the United States and China which is 7,245 raised to the 1.25 power equal to $284,621.51 billion.) billion.
Video transcript

Work It Out, Chapter 6, Question 1

(Transcript of audio with descriptions. Transcript includes narrator headings and description headings of the visual content)

(Speaker)
This problem will ask you to solve for the expected level of trade between the United States and Japan, and the United States and China, using the gravity equation. Let’s look at the information given. We’re told that the value of the constant B is equal to 93 and that the exponent we will use on the distance, n, is equal to 1.25.

(Description)
The following text is written: Gravity equation constant and exponent: B equals 93, n equals 1.25.

(Speaker)
We’re also given the 2015 GDPs of China, Japan, and the United States, in billions of dollars, and the distance from the United States of both China and Japan.

(Description)
The following table is shown below the previous text: The table consists of 2 columns: GDP in 2015 (billions of dollars), Distance from the United States (miles) The table consists of 3 rows: China, Japan, United States. The row China has the following data: 11385, 7245. The row Japan has the following data: 4116, 6314. The row United States has the following data: 17968, dash.

(Speaker)
With this information, we’ll be able to solve for the expected levels of trade between the United States and Japan and between the United States and China. Recall that the gravity equation tells us the expected level of trade is equal to B, which is a constant that indicates the relationship between the gravity term and trade, multiplied by the gravity term, which is gross domestic product of country 1 (GDP1) multiplied by the gross domestic product of country 2 (GDP2) divided by the distance between the two countries raised to a power n (dist n).

(Description)
The following equation is written: Trade equals B multiplied by GDP subscript 1 multiplied by GDP subscript 2 divided by dist to the power of n.

(Speaker)
Now let’s solve to find the expected level of trade between the United States and Japan. This will equal 93, the given value of B, multiplied by the value of the gravity term, which is the GDP of Japan (4 thousand 116) times the GDP of the United States (17 thousand 968) divided by the distance between the United States and Japan (6 thousand 314) raised to the 1.25 power.

(Description)
The following equation is written below the previous one: Trade equals 93 multiplied by 4116 multiplied by 17968 divided by 6314 to the power of 1.25.

(Speaker)
Solving our equation, we get an expected level of trade between the United States and Japan of 122 hundred 201.72 billion dollars.

(Description)
The following relation is written below the previous equation: Trade equals 122 hundred 201.72 billion dollars.

(Speaker)
We can do the same to solve for the expected level of trade between the United States and China.

(Description)
The following equation is written: Trade equals B multiplied by GDP subscript 1 multiplied by GDP subscript 2 divided by dist to the power of n.

(Speaker)
This will equal 93, the given value of B, multiplied by the value of the gravity term, which is the GDP of China (11 thousand 385) times the GDP of the United States (17 thousand 968) divided by the distance between the United States and China (7 thousand 245) raised to the 1.25 power.

(Description)
The following equation is written below the previous one: Trade equals 93 multiplied by 1 multiplied by 17968 divided by 7245 to the power of 1.25.

(Speaker)
Solving our equation, we get an expected level of trade between the United States and China of 284 thousand 621.51 billion dollars.

(Description)
The following relation is written below the previous equation: Trade equals 284 thousand 621.51 billion dollars.

Question

b. ta+I6txcDCqeelQTSr9cNorXYKJnkqwFGiGPMrRYP1wIfAx2rIQXRWu2h3kb04dqqZpjDH3UDjyKQtRoapH3Zx+Dac71eY8qKNEU0geobTNgl0Mj5LNdGp4cdEUqn//iwLwEILTB91efzolPbzJTz3ZyGXUtxDztnhxgcpIAFZdgcHTpZMmFLaYuGK6tjPM4wQiaZUaSoGeKfJ1tsRr3qz0eb6tJHNRjtpEdmdMp85s8rb9CP7Pos4GNS1nVjohkEfl3Xl39dxtS9n32Exg7CYIHMAs=

4Ku6/nS8B0AVYfAJdj5i5ryx92q52zDyM0c5igMDue/rxHAwW98MAuNaPeE/D5fu28Z18vgd/vmRtE1b2xWrbWylDLGyvh+c9P0Sbw==
Correct. You would expect more trade between China and Japan than between China and the United States. This is because of the much shorter distance between China and Japan. Even though Japan’s GDP is much smaller than that of the United States, the short distance between China and Japan dominates the size effect.
Incorrect. You would expect more trade between China and Japan than between China and the United States. This is because of the much shorter distance between China and Japan. Even though Japan’s GDP is much smaller than that of the United States, the short distance between China and Japan dominates the size effect.
Video transcript

Work It Out, Chapter 6, Question 2

(Transcript of audio with descriptions. Transcript includes narrator headings and description headings of the visual content)

(Speaker)
This problem will ask you to determine whether the expected level of trade between China and Japan will be more that the expected level of trade between China and the United States, given the distance between China and Japan as 1 thousand 302 miles. It also will ask you to explain which variable, country size (in terms of GDP) or distance, drives your result.

(Description)
In order to answer this question, we will first need to return to our gravity equation and solve for the expected value of trade between China and Japan.

(Speaker)
The following equation is written: Trade equals B multiplied by GDP subscript 1 multiplied by GDP subscript 2 divided by dist to the power of n.

(Description)

(Speaker)
This will equal 93, the given value of B, multiplied by the value of the gravity term, which is the GDP of Japan (4 thousand 116) times the GDP of China (11 thousand 385) divided by the distance between Japan and China (1 thousand 302) raised to the 1.25 power.

(Description)
The following equation is written below the previous one: Trade equals 93 multiplied by 4116 multiplied by 11385 divided by 1302 to the power of 1.25.

(Speaker)
Solving our equation, we get an expected level of trade between the China and Japan of 557 thousand 220.90 billion dollars.

(Description)
The following relation is written below the previous equation: Trade equals 557 hundred 220.90 billion dollars.

(Speaker)
We can now compare this value to the value of the expected level of trade between China and the United States we calculated in part a. 557 hundred 220.90 billion dollars is greater than 284 hundred 621.51 billion dollars, so we can conclude that we would expect more trade between China and Japan than between China and the United States.

(Description)
The following text is written: 557 hundred 220.90 billion dollars is greater than 284 hundred 621.51 billion dollars. The expected level of trade between China and Japan is greater than the expected level of trade between China and the United States.

(Speaker)
Even though Japan’s GDP is much smaller than that of the United States, the short distance between China and Japan dominates the size effect.

(Description)
The following text is written below the previous one: Distance effect dominates size effect.