Chapter 6, Problem 3.6P

(a)

To determine

To calculate the nominal GDP for 2018.

Explanation of Solution

The price of sugarcane 2018 is $1.15 and quantity is 300. The price of Yo-yos is $4 and quantity is 750. The price of rum is $15 and quantity is 180. The price of peanuts is $2.50 and quantity is 450. The price of Harmonicas is $30 and quantity is 85. The price of Peanut butter is $5 and quantity is 85.

Since it is given that the one quarter of sugar cane produced is used for production of rum, the final quantity of sugar cane available for consumption is calculated as follows:

$\text{Quantity}=\text{Total production}-\left(\frac{\text{Total production}}{4}\right)$        (1)

Substitute the respective value in Equation (1) to calculate the quantity of sugar cane in the year 2018.

$\begin{array}{c}\text{Quantity}=300-\left(\frac{300}{4}\right)\\ =300-75\\ =225\end{array}$

Quantity of sugarcane in the year 2018 is 225 units.

Since it is given that the half of the peanut produced is used for production of peanut butter, the final quantity of peanut available for consumption is calculated as follows:

$\text{Quantity}=\text{Total production}-\left(\frac{\text{Total production}}{2}\right)$        (2)

Substitute the respective value in Equation (2) to calculate the quantity of peanut cane in the year 2018.

$\begin{array}{c}\text{Quantity}=450-\left(\frac{450}{2}\right)\\ =450-225\\ =225\end{array}$

Quantity of peanut in the year 2018 is 225 units.

When the price and quantity of goods produced in the economy are given, the nominal GDP can be calculated as the sum of product of price and quantity of each item in the economy. Nominal GDP can be calculated using the following equation:

$\text{Nominal GDP}=\left(\begin{array}{l}\left({\text{Price}}_{\text{sugarcane}}\times {\text{Quantity}}_{\text{sugarcane}}\right)+\left({\text{Price}}_{\text{Yo-yos}}\times {\text{Quantity}}_{\text{Yo-yos}}\right)+\\ \left({\text{Price}}_{\text{rum}}\times {\text{Quantity}}_{\text{rum}}\right)+\left({\text{Price}}_{\text{peanuts}}\times {\text{Quantity}}_{\text{peanuts}}\right)+\\ \left({\text{Price}}_{\text{harmonicas}}\times {\text{Quantity}}_{\text{harmonicas}}\right)+\left({\text{Price}}_{\text{peanut butter}}\times {\text{Quantity}}_{\text{peanut butter}}\right)\end{array}\right)$        (3)

Substitute the respective values in Equation (3) to calculate the nominal GDP in 2018.

$\begin{array}{c}{\text{Nominal GDP}}_{2018}=\left(\begin{array}{l}\left(\text{1}\text{.15}\times \text{225}\right)+\left(\text{4}\times \text{750}\right)+\\ \left(\text{15}\times \text{180}\right)+\left(2.50\times \text{225}\right)+\\ \left(\text{30}\times \text{85}\right)+\left(\text{5}\times 85\right)\end{array}\right)\\ =258.75+3,000+2,700+562.50+2,550+425\\ =9,496.25\end{array}$

The nominal GDP for 2018 is $9,496.25.

Economics Concept Introduction

Gross Domestic Product (GDP): GDP refers to the market value of all final goods and services that are produced in an economy during an accounting year.

Nominal GDP: Nominal GDP is the market value of all final goods and services produced in an economy during an accounting year, measured in the current prices.

(b)

To determine

To calculate the real GDP for 2016, 2017, and 2018 using 2016 as the base year and also the growth rate of real GDP.

Explanation of Solution

The price of sugarcane 2016 is $0.80 and quantity is 240. The price of Yo-yos is $2.50 and quantity is 600. The price of rum is $10 and quantity is 150. The price of peanuts is $2 and quantity is 500. The price of Harmonicas is $25 and quantity is 75. The price of Peanut butter is $4.50 and quantity is 100. The quantity of sugar cane in 2017 is 240 and 2018 is 300. The quantity of Yo-yos in 2017 is 700 and 2018 is 750. The quantity of rum in 2017 is 160 and 2018 is 180. The quantity of peanuts in 2017 is 450 and 2018 is 450.

The quantity of harmonicas in 2017 is 75 and 2018 is 85. The quantity of peanut butter in 2017 is 85 and 2018 is 85.

Table-1 shows the final quantity of sugarcane and peanut for the different years that are obtained using Equations (1) and (2).

Table -1

Year	Quantity of peanut	Quantity of sugarcane
2016	250	180
2017	225	180
2018	225	225

When the price and quantity of goods produced in the economy are given, the real GDP can be calculated as the sum of product of price in the base year and quantity in the current year for each item in the economy. Calculation of Real GDP in each year is shown below.

${\text{Real GDP}}_{2016}=\left(\begin{array}{l}\left({\text{Price}}_{\text{sugarcane}\left(2016\right)}\times {\text{Quantity}}_{\text{sugarcane}\left(2016\right)}\right)+\left({\text{Price}}_{\text{Yo-yos}\left(2016\right)}\times {\text{Quantity}}_{\text{Yo-yos}\left(2016\right)}\right)+\\ \left({\text{Price}}_{\text{rum}\left(2016\right)}\times {\text{Quantity}}_{\text{rum}\left(2016\right)}\right)+\left({\text{Price}}_{\text{peanuts}\left(2016\right)}\times {\text{Quantity}}_{\text{peanuts}\left(2016\right)}\right)+\\ \left({\text{Price}}_{\text{harmonicas}\left(2016\right)}\times {\text{Quantity}}_{\text{harmonicas}\left(2016\right)}\right)+\left({\text{Price}}_{\text{peanut butter}\left(2016\right)}\times {\text{Quantity}}_{\text{peanut butter}\left(2016\right)}\right)\end{array}\right)$

$\begin{array}{c}{\text{Real GDP}}_{2016}=\left(\begin{array}{l}\left(\text{0}\text{.80}\times 180\right)+\left(2.50\times 60\text{0}\right)+\\ \left(\text{10}\times \text{150}\right)+\left(2\times \text{250}\right)+\\ \left(25\times 7\text{5}\right)+\left(\text{4}\text{.50}\times 100\right)\end{array}\right)\\ =5,969\end{array}$

Thus, the real GDP for 2016 is $5,969.

${\text{Real GDP}}_{2017}=\left(\begin{array}{l}\left({\text{Price}}_{\text{sugarcane}\left(2016\right)}\times {\text{Quantity}}_{\text{sugarcane}\left(2017\right)}\right)+\left({\text{Price}}_{\text{Yo-yos}\left(2016\right)}\times {\text{Quantity}}_{\text{Yo-yos}\left(2017\right)}\right)+\\ \left({\text{Price}}_{\text{rum}\left(2016\right)}\times {\text{Quantity}}_{\text{rum}\left(2017\right)}\right)+\left({\text{Price}}_{\text{peanuts}\left(2016\right)}\times {\text{Quantity}}_{\text{peanuts}\left(2017\right)}\right)+\\ \left({\text{Price}}_{\text{harmonicas}\left(2016\right)}\times {\text{Quantity}}_{\text{harmonicas}\left(2017\right)}\right)+\left({\text{Price}}_{\text{peanut butter}\left(2016\right)}\times {\text{Quantity}}_{\text{peanut butter}\left(2014\right)}\right)\end{array}\right)$

$\begin{array}{c}{\text{Real GDP}}_{2017}=\left(\begin{array}{l}\left(\text{0}\text{.80}\times 180\right)+\left(2.50\times 70\text{0}\right)+\\ \left(\text{10}\times \text{160}\right)+\left(2\times \text{225}\right)+\\ \left(25\times 7\text{5}\right)+\left(\text{4}\text{.50}\times 85\right)\end{array}\right)\\ =6,201.50\end{array}$

Thus, the real GDP for 2017 is $6,201.50.

${\text{Real GDP}}_{2018}=\left(\begin{array}{l}\left({\text{Price}}_{\text{sugarcane}\left(2016\right)}\times {\text{Quantity}}_{\text{sugarcane}\left(2018\right)}\right)+\left({\text{Price}}_{\text{Yo-yos}\left(2016\right)}\times {\text{Quantity}}_{\text{Yo-yos}\left(2018\right)}\right)+\\ \left({\text{Price}}_{\text{rum}\left(2016\right)}\times {\text{Quantity}}_{\text{rum}\left(2018\right)}\right)+\left({\text{Price}}_{\text{peanuts}\left(2016\right)}\times {\text{Quantity}}_{\text{peanuts}\left(2018\right)}\right)+\\ \left({\text{Price}}_{\text{harmonicas}\left(2016\right)}\times {\text{Quantity}}_{\text{harmonicas}\left(2018\right)}\right)+\left({\text{Price}}_{\text{peanut butter}\left(2016\right)}\times {\text{Quantity}}_{\text{peanut butter}\left(2018\right)}\right)\end{array}\right)$

$\begin{array}{c}{\text{Real GDP}}_{2018}=\left(\begin{array}{l}\left(\text{0}\text{.80}\times 225\right)+\left(2.50\times 75\text{0}\right)+\\ \left(\text{10}\times \text{180}\right)+\left(2\times \text{225}\right)+\\ \left(25\times 8\text{5}\right)+\left(\text{4}\text{.50}\times 85\right)\end{array}\right)\\ =6,812.50\end{array}$

Thus, the real GDP for 2018 is $6,812.50.

The real GDP growth rate between 2016 and 2017 can be calculated using the following equation:

$\begin{array}{c}\text{Growth in real GDP}=\frac{{\text{Real GDP}}_{2017}-{\text{Real GDP}}_{2016}}{{\text{Real GDP}}_{2016}}\times 100\\ =\frac{\left(6,201.50-5,969\right)}{5,969}\times 100\\ =3.90\end{array}$

The real GDP growth rate between 2016 and 2017 is 3.90%.

The real GDP growth rate between 2017 and 2018 can be calculated using the following equation:

$\begin{array}{c}\text{Growth in real GDP}=\frac{{\text{Real GDP}}_{2018}-{\text{Real GDP}}_{2017}}{{\text{Real GDP}}_{2017}}\times 100\\ =\frac{\left(6,812.50-6,201.50\right)}{6,201.50}\times 100\\ =9.85\end{array}$

The real GDP growth rate between 2017 and 2018 is 9.85%.

Economics Concept Introduction

Real GDP: Real GDP refers to the market value of all the final goods and services produced in an economy during an accounting year, which is measured in constant prices.

(c)

To determine

To calculate the real GDP for 2016, 2017, and 2018 using 2017 as the base year and also the growth rate of real GDP.

Explanation of Solution

Base year is 2017 in Table-1. When the price and quantity of goods produced in the economy are given, the real GDP can be calculated as the sum of product of price in the base year and quantity in the current year for each item in the economy. Real GDP can be calculated using the following equation:

${\text{Real GDP}}_{2016}=\left(\begin{array}{l}\left({\text{Price}}_{\text{sugarcane}\left(2017\right)}\times {\text{Quantity}}_{\text{sugarcane}\left(2016\right)}\right)+\left({\text{Price}}_{\text{Yo-yos}\left(2017\right)}\times {\text{Quantity}}_{\text{Yo-yos}\left(2016\right)}\right)+\\ \left({\text{Price}}_{\text{rum}\left(2017\right)}\times {\text{Quantity}}_{\text{rum}\left(2016\right)}\right)+\left({\text{Price}}_{\text{peanuts}\left(2017\right)}\times {\text{Quantity}}_{\text{peanuts}\left(2016\right)}\right)+\\ \left({\text{Price}}_{\text{harmonicas}\left(2017\right)}\times {\text{Quantity}}_{\text{harmonicas}\left(2016\right)}\right)+\left({\text{Price}}_{\text{peanut butter}\left(2017\right)}\times {\text{Quantity}}_{\text{peanut butter}\left(2016\right)}\right)\end{array}\right)$

$\begin{array}{c}{\text{Real GDP}}_{2016}=\left(\begin{array}{l}\left(\text{1}\times 180\right)+\left(3\times 60\text{0}\right)+\\ \left(\text{12}\times \text{150}\right)+\left(2.50\times \text{250}\right)+\\ \left(30\times 7\text{5}\right)+\left(\text{4}\text{.50}\times 100\right)\end{array}\right)\\ =7,105\end{array}$

Thus, the real GDP for 2016 is $7,105.

${\text{Real GDP}}_{2017}=\left(\begin{array}{l}\left({\text{Price}}_{\text{sugarcane}\left(2017\right)}\times {\text{Quantity}}_{\text{sugarcane}\left(2017\right)}\right)+\left({\text{Price}}_{\text{Yo-yos}\left(2017\right)}\times {\text{Quantity}}_{\text{Yo-yos}\left(2017\right)}\right)+\\ \left({\text{Price}}_{\text{rum}\left(2017\right)}\times {\text{Quantity}}_{\text{rum}\left(2017\right)}\right)+\left({\text{Price}}_{\text{peanuts}\left(2017\right)}\times {\text{Quantity}}_{\text{peanuts}\left(2017\right)}\right)+\\ \left({\text{Price}}_{\text{harmonicas}\left(2017\right)}\times {\text{Quantity}}_{\text{harmonicas}\left(2017\right)}\right)+\left({\text{Price}}_{\text{peanut butter}\left(2017\right)}\times {\text{Quantity}}_{\text{peanut butter}\left(2017\right)}\right)\end{array}\right)$

$\begin{array}{c}{\text{Real GDP}}_{2017}=\left(\begin{array}{l}\left(\text{1}\times 180\right)+\left(3\times 70\text{0}\right)+\\ \left(\text{12}\times \text{160}\right)+\left(2.50\times \text{225}\right)+\\ \left(30\times 7\text{5}\right)+\left(\text{4}\text{.50}\times 85\right)\end{array}\right)\\ =7,395\end{array}$

Thus, the real GDP for 2017 is $7,395.

${\text{Real GDP}}_{2018}=\left(\begin{array}{l}\left({\text{Price}}_{\text{sugarcane}\left(2017\right)}\times {\text{Quantity}}_{\text{sugarcane}\left(2018\right)}\right)+\left({\text{Price}}_{\text{Yo-yos}\left(2017\right)}\times {\text{Quantity}}_{\text{Yo-yos}\left(2018\right)}\right)+\\ \left({\text{Price}}_{\text{rum}\left(2017\right)}\times {\text{Quantity}}_{\text{rum}\left(2018\right)}\right)+\left({\text{Price}}_{\text{peanuts}\left(2017\right)}\times {\text{Quantity}}_{\text{peanuts}\left(2018\right)}\right)+\\ \left({\text{Price}}_{\text{harmonicas}\left(2017\right)}\times {\text{Quantity}}_{\text{harmonicas}\left(2018\right)}\right)+\left({\text{Price}}_{\text{peanut butter}\left(2017\right)}\times {\text{Quantity}}_{\text{peanut butter}\left(2018\right)}\right)\end{array}\right)$$\begin{array}{c}{\text{Real GDP}}_{2015}=\left(\begin{array}{l}\left(\text{1}\times 225\right)+\left(3\times 75\text{0}\right)+\\ \left(\text{12}\times \text{180}\right)+\left(2.50\times \text{225}\right)+\\ \left(30\times 8\text{5}\right)+\left(\text{4}\text{.50}\times 85\right)\end{array}\right)\\ =8,130\end{array}$

Thus, the real GDP for 2018 is $8,130.

The real GDP growth rate between 2016 and 2017 can be calculated using the following equation:

$\begin{array}{c}\text{Growth in real GDP}=\frac{{\text{Real GDP}}_{2017}-{\text{GDP}}_{2016}}{{\text{GDP}}_{2016}}\times 100\\ =\frac{\left(7,395-7,105\right)}{7,105}\times 100\\ =4.08\end{array}$

The real GDP growth rate between 2016 and 2017 is 4.08%.

The real GDP growth rate between 2017 and 2018 can be calculated using the following equation:

$\begin{array}{c}\text{Growth in real GDP}=\frac{{\text{Real GDP}}_{2018}-{\text{GDP}}_{2017}}{{\text{GDP}}_{2017}}\times 100\\ =\frac{\left(8,130-7,395\right)}{7,395}\times 100\\ =9.94\end{array}$

The real GDP growth rate between 2017 and 2018 is 9.94%.