# Population growth vs. food supply growth

Institute for Environmental and Spatial Analysis...University of North Georgia

Contents

## 1 Population growth

- The world population in 2018 was 7.6 billion.
- The population growth rate is approximately 1.09% or 0.0109.
- $\mathrm{Pop}(y_c+1)=\mathrm{Pop}(y_c)\times(1+r_\text{pop})$
- where $y_c$ is the current year and $r_\text{pop}$ is the growth rate.

- The population grows exponentially.
- So... the population in a future year $y_f$ can be estimated using \[\mathrm{Pop}(y_f)=\mathrm{Pop}(y_c)\times(1+r_\text{pop})^{y_f-y_c}\]

### 1.1 Population question

Estimate the world population in 2050.

## 2 Food supply growth

Thomas Malthus (an 18th century English scholar) observed:

- The growth of human population is fundamentally different from that of food supply.
- The food supply grows arithmetically (linearly).
- $\mathrm{Food}(y_c+1)=\mathrm{Food}(y_c)+\mathrm{Food}(y_c)\times r_\text{food}$
- where $r_\text{food}$ is the growth rate of food supply.

- Generalizing this equation yields \[\mathrm{Food}(y_f)=\mathrm{Food}(y_c)\left[1+r_\text{food}\times(y_f-y_c)\right]\]

### 2.1 Food supply question

- Let’s assume that $\mathrm{Food}(2018)$ can feed 110% of the 2018 world population and the growth rate of food supply is 1%.
- Estimate the food supply in 2050 in the amount equivalent to population.
- In what year, is the world population most likely to outgrow the food supply?

## 3 Population vs. food supply

Try this Excel.