Macroeconomics Malthus’s Model of Growth - New York University

Macroeconomics Malthus's Model of Growth

Practice Problems #0

? Questions?

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"Guard your manhood"

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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

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 K L1- Y/L = A (K/L)

? Questions

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

Malthus's model: production

? 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: production

Malthus's model: production

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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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Malthus's model: population

? To keep things simple

? 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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Malthus's model: population

Malthus's model: population

? 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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Malthus's model: population

Malthus's model: production

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What if we reduce mortality?

? How does that show up on the graph that follows? ? What do you think happens?

? To population? ? To income? ? To income per person?

? Think about how the model works

Malthus's model: population

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What if we increase productivity?

? How does that show up on the graph that follows? ? What do you think happens?

? To population? ? To income? ? To income per person?

? Think about how the model works

Malthus's model: production

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Malthus's model: population

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)

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