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# Population growth vs. food supply growth

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

## 1   Population growth

Current world population

• 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?

Try this Excel.