macroeconomics malthus’s model of...

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Macroeconomics

Malthus’s Model of Growth

Practice Problems #0

• Questions?

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“Guard your manhood”

• https://www.depend.com/guard-your-manhood/#home

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Malthus & his model

Malthus

• English “philosopher” and “political economist”

• Lived 1766-1834

• Ordained minister

– Concerned with the poor

– England had lots of poor

• Original “dismal scientist”

• Dead wrong – afterwards

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Models

• Model = a specific implementation of a theory

– A way of organizing our thoughts

– Uses equations to be precise

– Simplicity is good: strip away details [we can always add them back in later]

– A laboratory for asking “what if?”

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What Malthus knew

• J Hatcher:

– Between Domesday [1086] and the Black Death, the population of England rose from just under 2 million to about 4 million. Land was scarce, wages and the standard of living were low. Then in 1348-1349 the Black Death reduced the population by about 60%. [In the century that followed] wage levels rose to previously unknown heights, as did the general standard of living.

• What’s going on? Why did living standards rise?

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Malthus’s growth model

• Picture of the world

– Everyone’s a farmer

– Growing food to eat

• Ingredient 1: production function

– Relate output to labor input

– Larger population => more workers => higher output => lower income per person

• Ingredient 2: population dynamics

– Population adds births, subtracts deaths

– Death rate lower if incomes are higher

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Malthus’s model: production

• Production function

Y = A Kα L1-α

Y/L = A (K/L)α

• Questions

– What is α?

– What happens to Y/L as we increase L?

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• To keep things simple

– Everyone works (L=POP)

– Capital K =1000 is constant (land)

– Productivity A = 79.37 also constant (don’t ask)

– Initial population L0 arbitrary (millions)

• See spreadsheet

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Malthus’s model: population

• Things that change population

– Births (B) increase population (L)

– Deaths (D) decrease population (L)

• Population

Lt+1 = Lt + Bt − Dt

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– Birth rate constant

– Death rate declines with income (increases with population)

• Birth and death rates

Bt /Lt = b

Dt/Lt = d0 + d1 (1000 − Lt)

• Numbers: b = 0.05, d0 = 0.05, d1 = 0.0001

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• Questions for the figure

– On the left (right), is population high or low

– Is population increasing or decreasing?

– Is income per person increasing or decreasing?

– Which way are we moving in the figure?

– Where do we end up?

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Experiments

What if we start with low population?

• Where is that on the graph that follows?

• What do you think happens?

– To population?

– To income?

– To income per person?

• Think about how the model works

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What if we reduce mortality?

• How does that show up on the graph that follows?


– To population?

– To income?



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What if we increase productivity?



– To population?

– To income?



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Bottom line

• None of these things raise long-term living standards

• If there’s a lot to eat, more people will arrive to eat it [“If you grow it, they will come”]

• Biologists have similar models for flies, rabbits, etc

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Assessment

What happened?

• In the UK

– Population increased by a factor of 5

– Income per person increased by a factor of 20!

– Agriculture became less important

• Oops!

• Where did we go wrong?

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Where did Malthus go wrong?

• Incomes rose (massive increases in productivity) [unprecedented]

• Demographics changed: as people became richer, they had fewer children [also unprecedented – see Gapminder]

• Something to think about

– How important was China’s one-child policy to its rapid growth?

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Takeaways

• Malthus had a nice theory for the period before 1800

• Since then, not so much

– Enormous productivity growth

– Dramatic change in demographics

• How should we think about that?

Y/L = A (K/L)α

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For next class

• Should we save more?

– As individuals or as countries?

– Why? Or why not?

– Examples?

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Macroeconomics



• Questions?

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Malthus & his model

Malthus


• Lived 1766-1834






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Models






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2

What Malthus knew

• J Hatcher:



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Y = A Kα L1-α

Y/L = A (K/L)α

• Questions

– What is α?


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• See spreadsheet

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• Population


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Bt /Lt = b

Dt/Lt = d0 + d1 (1000 − Lt)

• Numbers: b = 0.05, d0 = 0.05, d1 = 0.0001

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Experiments




– To population?

– To income?



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– To population?

– To income?



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– To population?

– To income?



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Bottom line




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Assessment

What happened?

• In the UK




• Oops!


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Takeaways






Y/L = A (K/L)α

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