Question

the changing lives of american farmers
interpreting statistics
agricultural productivity
1800 1900
wheat
worker - hours to produce an acre 56 15
yield per acre 15 14
corn
worker - hours per acre 80 38
yield per acre 25 26
cotton
worker - hours per acre 185 112
yield per acre 147 191
questions to think about

1. how great was the increase in agricultural productivity between 1800 and 1900?
2. why did agricultural productivity increase between 1800 and 1900?
3. describe the social and economic consequences of increasing agricultural productivity?

Explanation:

Step1: Define productivity

Productivity can be related to yield per worker - hour. Calculate yield per worker - hour for each crop in 1800 and 1900.
For wheat in 1800: $\frac{15}{56}\approx0.27$ (yield per worker - hour)
For wheat in 1900: $\frac{14}{15}\approx0.93$
For corn in 1800: $\frac{25}{80} = 0.3125$
For corn in 1900: $\frac{26}{38}\approx0.68$
For cotton in 1800: $\frac{147}{185}\approx0.79$
For cotton in 1900: $\frac{191}{112}\approx1.71$

Step2: Calculate overall productivity increase

Find the average of the productivity ratios for each crop.
Average of productivity ratios: $\frac{(0.93/0.27)+(0.68/0.3125)+(1.71/0.79)}{3}$
$=\frac{(3.44)+(2.18)+(2.16)}{3}=\frac{7.78}{3}\approx2.59$ - fold increase in overall agricultural productivity.

Step3: Reasons for productivity increase

Technological advancements like better farming tools, improved seeds, and more efficient irrigation systems were major factors. Also, the spread of agricultural knowledge and the development of new farming techniques contributed.

Step4: Social and economic consequences

Social: Migration from rural to urban areas as fewer workers were needed in agriculture. Change in the social structure of rural communities. Improved living standards due to increased food availability.
Economic: Lower food prices due to increased supply, which increased the real - income of consumers. Growth of related industries such as food processing and agricultural machinery manufacturing.

Answer:

1. Approximately 2.59 - fold increase in overall agricultural productivity between 1800 and 1900.
2. Technological advancements, spread of knowledge, and new farming techniques.
3. Social: Migration, change in social structure, improved living standards. Economic: Lower food prices, growth of related industries.