Ten Farmers Model of Macroeconomics | Tom Cunningham

I came up with this 10-farmer parable in 2010 when I was teaching assistant for Macroeconomics 1010b. I am not a macroeconomist and it’s very likely that I am butchering the literature.

Nevertheless I have personally found it a useful and versatile mental model. Whenever I need to think about some question involving the economy as a whole (general equilibrium) I think of a set of farmers trading peaches and potatoes.
A very compressed version:

Tonight the baker eats just what she baked ‍‍‍‍‍‍‍‍
The fisherman eats just what he caught
Because this morning at the market
Everyone tried to sell more than they bought.

INTRODUCTION

The big puzzle of macroeconomics is why the web of exchange sometimes abruptly shrinks, leaving empty factories, fallow fields, unemployed workers, without any tangible cause. The most accepted theory is that it’s the fault of the slowness with which prices and wages change.
Here I give a simple parable about 10 farmers to give the intuition why this sluggishness in prices can cause the network of exchange to shrink, i.e. a recession. It also tries to explain the logic behind interventions in the economy, monetary and fiscal policy, intended to smooth out recessions. I then try to talk about the 2007-2009 recession.
After the parable I state a simple formal model to make explicit the assumptions being used. Finally I discuss a list of related economic issues, and how the basic story can be used to make sense of them.

SETUP

Imagine a village with ten identical farms, each of which starts off as self-sufficient: each grows their own wheat, herds their own sheep, raises their own tomatoes, etc.. However each farmer gradually discovers that they can become better off by specializing: if your household were to concentrate just on growing wheat then you could grow it very efficiently, and exchange that wheat for vegetables and meat and whatever else you need.
So suppose the village organizes a market every Saturday where everyone brings the thing they produce: the farmer sells her wheat, the shepherd sells her sheep, the market gardener sells his tomatoes.
Every Saturday morning each farmer brings 10 sacks of their crops to the market, and at the end of each Saturday they bring home 1 sack of their own crop, and the 9 sacks of the others’ crops that they’ve bought in exchange.
And finally suppose that they use sea shells as a form of money. Each farmer owns 10 shells, and over the course of a Saturday they use these shells to buy others’ vegetables, and receive shells in return for their own, so that at the end of the day each farmer returns home with 10 shells. Suppose that the price of all vegetables is the same, 1 shell per sack of vegetables. The price of crops will naturally be proportional to the number of shells in circulation: if each farmer had 100 shells, instead of 10, then then the price of each sack would be 10 shells.

RECESSIONS

Suppose that one Saturday morning every farmer decides they would prefer to buy fewer crops, and so save more shells, than usual. This could be for any reason: because each expects a harsh winter, or because each is saving for a wedding. Each farmer will therefore arrive to the market with the intention to buy fewer goods, and save more shells, than usual.
Now, it is possible for any one farmer to return home with more shells than they arrived with, but it is not possible for every farmer to return home with more shells than they arrived with, because there are only a fixed number of shells available.
Suppose that, at first, each farmer maintained the same price of 1 shell/bag. Because each farmer arrives with a higher demand for shells than usual, they will buy less vegetables than usual, but they will also sell fewer vegetables than usual.
Because the farmer wants more shells, it will make sense to cut their prices, to get rid of their surplus crops in exchange for more shells. The lower prices will tempt each farmer to spend more of their shells, because it’s cheaper to buy the other guys’ goods. The price must keep dropping as long as each farmer has more of their own vegetables than others’, until eventually each farmer has 10 shells and 10 sacks of crops, one of each type of vegetable. When every farmer wants to spend less, aggregate expenditure won’t change, the only effect will be that prices fall.

STICKY PRICES

Now suppose instead that the farmers were not able to change their prices: for example, if each farmer has already advertised their price (one shell per sack) and they feel obliged not to cut the price. Each farmer will buy less, and each farmer will sell less, and so at the end of Saturday each farmer will return home with more of their own vegetables than others’ vegetables. There will be less overall exchange, and the farmers will be all worse off: the children of the carrot farmer will have to eat carrot soup for breakfast, carrot cake for lunch, and carrot pie for dinner. When prices cannot change then a fall in the desire to spend causes a fall in the amount of goods exchanged, making everyone worse off.
Next week if the prices are allowed to change they will all fall, and the amount of goods exchanged will bounce back, but in the meantime there is a slump in the quantity of goods exchanged, and all of the farmers will be unnecessarily worse off.
The observation that prices change slowly, and this causes unnecessary fluctuations in exchange, is the core dogma of orthodox macroeconomics.

ANTI-RECESSION POLICY

The mayor of the village is distressed: she sees that the carrot farmer’s children are sick of eating carrots, and the shepherd has a barn full of rotting mutton. She sees that everyone could be better off, but the system of exchange is not working as it normally does. What can she do to prevent so much waste? Ideally she would find some way of allowing people to drop their prices, or to force the prices down. However the problem would also be solved if she could somehow persuade every farmer to spend more money, because the stickiness of prices has turned the situation into a tragedy of the commons: each farmer is spending as much as they would like to, but if all the farmers were to spend more then they would also all sell more, and this would make them all better off. So the task of fighting recessions is often described as persuading people to spend more money.
monetary policy. Because the problem is that the old level of prices is too high for today’s demand, an elegant solution is to simply change today’s demand to make the old prices the correct prices. This the mayor does by collecting shells from the beach, stamping them with her official mark, and handing them to each farmer as they arrive on Saturday morning.¹ If prices were not sticky then increasing the amount of money would simply cause an exactly proportional increase in prices: if, for example, the mayor doubled the number of shells in circulation, then prices would double. However because prices are slow to change, giving each farmer more shells will make it relatively more attractive for each farmer to spend. If the Mayor is able to choose just the correct amount of shells, then farmers will spend enough to return to the original state, in which each farmer returns home with one sack of each type of vegetable, and everyone is made better off.²
As we said, monetary policy can be thought of as changing the market conditions, so that the fixed level of prices becomes the price level at which a healthy level of exchange takes place. Thus as mayor you could instruct the head of the village Mint to follow this policy: from week to week, increase or decrease the quantity of shells necessary to keep the average level of prices stable. This policy should offset any fluctuations of demand, and should keep the level of exchange at an efficient level. This is roughly the doctrine of modern central banks: they try to manage the money supply so that the average price level remains constant, or more commonly, so that it slowly grows at a predictable rate, e.g., a 2% rate of inflation.
fiscal policy. An alternative solution to the problem is for the mayor to stand by the village gates on a Saturday morning, and as each farmer passes, confiscate some amount of shells from each one. The Mayor then uses the confiscated shells to buy vegetables off the farmers which she distributes to the town. As a farmer you end up with the same number of shells, because for every shell you lose in taxation, the government pays you a shell for your produce. But instead of returning home with your unsold produce, it is now owned by the mayor, who then distributes it for free.³ This policy (fiscal policy) is usually regarded as a less efficient way of countering out recessions than monetary policy, because the distribution of vegetables is now determined by the mayor, instead of the farmers themselves.⁴
It is very important to keep in mind that these stimulative policies only make sense when prices are fixed. If we assume prices are flexible, as is done in classical economic analysis, then neither fiscal nor monetary policy make any sense at all. Printing money will only increase prices, it will not increase exchange. Taxing in order to spend will just change who controls the distribution of vegetables, it will not increase the overall amount of vegetables exchanged.⁵ If we assume that in the long-run all prices adjust to their equilibrium levels, then these policies will only work temporarily, while prices are stuck at their old levels.

¹ Newly created money is not usually given away, instead it is used to buy bonds, but the effect is similar, and the profit made from creating new money is usually quite small relative to other taxes.

² Note that farmers are still not saving any more, their net savings are zero.

³ Note, this is equivalent to balanced-budget fiscal policy. In fact it is more common to use deficit-financed spending, in which you borrow shells off each farmer, to buy food now, and repay the shells later, by taxing the farmers in the future.

⁴ There may be other reasons for the mayor to put on a regular feast, but here we are just interested in tools to fight a recession.

⁵ Or if it does, not in a beneficial way (discussed below).

IN A NUTSHELL

The overall level of prices reflects how much people value money relative to goods and services. When that tradeoff changes, for example when people have a lower desire to spend today, then the equilibrium level of prices will change, but there should be little effect on the amount exchanged. However if prices are fixed then a fall in the desire to spend will cause a contraction in the volume of goods and services exchanged, leaving everyone worse off. The volume of exchange can be reinflated either by printing and distributing more money, or by the Government enforcing exchange through tax and spending.
More precisely: why did I have a job at Starbucks in 2007, but no job in 2009? The answer is that everyone stopped spending money, yet prices and wages remained the same instead of falling. As a consequence many previously profitable jobs became unprofitable, i.e., people were willing to buy fewer cups of coffee at the 2007 price. Then why didn’t Starbucks just cut their prices and wages, to sell the same amount of coffee, instead of laying off workers and closing stores? This remains a fundamental puzzle, some theories, discussed below, are (i) because the effect on Starbucks’ profit is small, even though the effect on employment may be large; (ii) because Starbucks doesn’t want to cut their prices or wages without other firms cutting theirs at the same time; and (iii) firms are particularly reluctant to cut wages because it has a bad effect on morale.

THE STICKINESS OF PRICES

The slowness of prices to change is the single essential ingredient of the mainstream of macroeconomic theory since the middle of the 20th century (often called “Keynesian” or “new Keynesian”, though the idea was explained at least as early as Hume). From here on, when I say “price” I mean both prices and wages, because a wage is just a price for labour. The general belief by economists in the sluggishness of prices, usually called price stickiness, is based on two observations (a third observation is that if prices are sticky, this could explain why we have unemployment).
The first observation is simply that most prices and wages change very gradually over time, whereas supply and demand can change rapidly. The wholesale prices of oil and wheat fluctuate a great deal from day to day, but this is not the norm, most prices are extremely stable. Think of the prices of a pack of spaghetti, a pizza from a restaurant, the price of a telephone connection, the price of a t-shirt, or the wage needed to hire a dish-washer: these prices mostly remain the same month to month, even from year to year, despite changes in supply and demand for each good. The reason why prices and wages move so slowly remains a subject of argument.
The second observation is a pattern in historical economic data: recessions (i.e. periods of low GDP and high unemployment) tend to occur at the same time that prices are falling, and booms tends to occur at the same time that prices are rising (i.e., during periods of inflation). This empirical relationship is called the Phillips curve, after a paper by A.W. Phillips in 1953, and it is what the story above predicts: when people are trying to spend less then prices will tend to fall, but won’t fall instantaneously, so there will be a period of low exchange and falling prices. Likewise when there is an overall increase in spending the amount of goods exchanged will be temporarily higher than usual, and over that period prices will be rising to catch up.⁶

⁶ In the 1970s many developed countries had a period of “stagflation”: simultaneous high inflation and high unemployment, which is not predicted by the Phillips curve. This is usually interpreted as being due to an increase in inflation expectations: if people are expecting prices to increase by 15%, then a fall in demand may cause prices to increase by only 10% instead. The Phillips curve can be reinterpreted as a good description of the difference between actual and expected inflation.

APPLIED TO THE US RECESSION OF 2007-09

Here is a simplified story, transposed from the village market, to the US economy in 2007.
Think of a typical American family in 2007, who earns $4,000 per month.⁷ The national average savings rate was around 0%, meaning that families spent their entire income. The low desire to save was probably due to the prices of houses, which had been increasing at 10% per year, and since most families owned houses, this seems to have reflected optimism about the future in some sense. However in mid 2006 house prices stopped rising, i.e. the optimism started to peter out, and in during 2007 people started to cut back spending, and therefore increase saving.
Many people cut back their spending by about 5% by, for example, deciding not to buy a new house, not buying a new car, to less often buy a coffee on the way to work, or to not buy a new laptop. Thus, at the existing level of prices and wages, there was less demand for goods and services, and people started losing jobs (the construction worker, the car manufacturer, the coffee maker, and the laptop seller).
The original level of employment and output could be restored if both wages and prices fell in response to reflect the lower demand for goods and services relative to money; the lower level of prices and wages would cause people to spend more money, restoring the balance. However prices and wages did not fall, they remained quite flat. So employment (and hence GDP) fell by 5% between summer 2007 and summer 2009.
Remember that GDP is principally a measure of the value of goods and services produced for exchange. So when GDP falls it means that the extent of exchange has contracted: it means that many people are at home, cooking themselves meals, entertaining themselves, and polishing their own nails, instead of entering into the huge network of exchange; likewise office buildings, roads, factories and telephone lines all suddenly became unused.
The following policies were used to try to restore employment and output:
1. the Federal reserve increased its lending of money, from $1Tn to $2Tn ($10,000 per household)
2. the Federal government rebated around $1Tn of taxes in 2008 and 2009 to households ($10,000 per household)
3. the Federal government spent around $500Bn in 2008 and 2009 on new projects ($5,000 per household, although at the same time state and local spending decreased by about the same amount)
4. finally, the Federal government has been spending around $100Bn extra in unemployment benefits per year since 2008 ($1,000 per household per year)
In fact, despite these policies, employment and GDP have only recovered very slowly towards to their previous levels. Some say this is because the policies were not effective; others say that the recession would have been worse without them.

⁷ In 2007 there were 100 million households in the US, with average income of $150,000, median income of $50,000 (FRED).

A FORMAL MODEL

Here I will briefly describe a mathematical version of the parable. The model is not necessary for understanding the parable, but it helps in making clear a set of assumptions sufficient to produce the behaviour described. In brief, suppose an economy has farmers who are identical except for producing differentiated goods, who have a desire to hold real money balances, and who price their goods competitively, but the sellers must commit to prices in advance. Then an exogenous increase in the demand for money will cause the volume of exchange to fall, a Pareto-dominated outcome. The efficient equilibrium can be restored by increasing the money supply.

In more detail: suppose there are two farmers, $i\in\{b,g\}$, who are each able to produce $\bar{x}$ sacks of beef and grain each per week respectively. They also both hold money, $m_{i}$, and I represent their preferences with $U_{i}=\sum_{j\in\{b,g\}}\ln(x_{i}^{j})+\gamma\ln(\frac{m_{i}}{p})$, where $x_{i}^{j}$ represents farmer $i$’s consumption of good $j$, and $p$ is the overall price level, $p=\frac{1}{2}\sum_{j\in\{b,j\}}p_{j}$. The game has three stages: first, both farmers simultaneously choose the price of their own good ($p^{j}$) – and I assume that prices are set competitively (i.e., prices clear markets based on submitted demand and supply schedules); second, the demand for money ($\gamma$) is realised; finally, both farmers simultaneously choose how much to buy from the other farmer at the posted price. The farmers’ budget constraints will be (for $j\neq i$, and with $m_{0}$ being the money endowment of both farmers): \[\begin{aligned} \mbox{income} & = & \mbox{expenditure}\\ \mbox{initial money}+\mbox{money earned} & = & \mbox{final money}+\mbox{money spent}\\ m_{0}+x_{j}^{i}p^{i} & = & m_{i}+x_{i}^{j}p^{j}\end{aligned}\] If both farmers maximiZe their utility then the marginal benefit of holding a good ($\frac{1}{x_{i}^{j}}$) will equal its marginal cost ($\gamma\frac{p^{j}}{m_{i}}$), so each farmer has a demand function, \[x_{i}^{j}=\frac{m_{i}}{\gamma p^{j}}=\frac{x_{j}^{i}p^{j}+m_{0}}{\left(1+\gamma\right)p^{j}}\] with a marginal propensity to consume from income of $\frac{1}{1+\gamma}$. For a given $p^{i},p^{j}$, equilibrium is shown on the diagram. The symmetric equilibrium (with $x_{b}^{g}=x_{g}^{b}$, $p^{b}=p^{g}$, $m=m_{0}$), will have $x_{b}^{g}=x_{g}^{b}=\frac{m_{0}}{\gamma p}$, i.e. for a given price level, output will be increasing in the supply of money, and decreasing in the demand for money ($\gamma$).

Suppose first that prices are flexible (equivalently, suppose that $\gamma$ is as expected). A Pareto-optimal equilibrium would be for each farmer to have identical consumption baskets, i.e., $x_{b}^{g}=x_{g}^{b}=\frac{\bar{x}}{2}$. In this case prices must be $p=\frac{2m_{0}}{\gamma\bar{x}}$, implying that if there is an exogenous change in money supply or money demand ($m_{0}$ or $\gamma$), then prices will move to exactly offset the change, and restore efficiency.

Alternatively suppose that $\gamma$ changes after prices are set. When prices are below their efficient level we are now in a prisoner’s dilemma: both farmers would be made better off if they could agree to spend more money, but it is not in either farmer’s own interest to spend more. Monetary policy, through changing $m_{0}$, can return the economy to the efficient level of exchange.

You could think of fiscal policy as working by confiscating money and buying goods, which are then handed out; in the budget constraint your money will be unchanged, but $x_{i}^{j}$ and $x_{j}^{i}$ will both exogenously increase by the same amount.

NOTES & EXTENSIONS

Recessions in a sentence: On the way out the door every farmer’s wife says to every farmer, “the weather’s looking bad so don’t buy as much at the market this week, but also don’t sell our crops for less than the usual price.”

Stimulus in a sentence: the mayor confiscates all the unsold food and puts on a feast.
Making sense of macroeconomic arguments. When discussing macroeconomic issues in this framework it is extremely important to be clear about the distinction between the “short-run” and “long run”, which are used to refer to the model in which prices are fixed, and the model in which prices are free to adjust. The effects of a policy will often be completely different in the short-run and the long-run, and confusing these two issues is a large reason why macroeconomic policy discussion can be so confusing. Here are some common issues explained with reference to the parable of the vegetable farmers.
1. “job creation” – why should we want to create jobs? Isn’t it better if we can work less, rather than more, everything else equal? In the long run the number of jobs simply reflects the amount of work done for exchange (rather than for yourself), and is determined by the returns to specialization. However in the short-run employment can fall because of a lack of demand, and so during a recession the quantity of jobs has a different significance: it now indicates the progress in recovering from a slump in demand. Work isn’t desirable in itself, but the amount of work done is an indicator of the health of the economy, so that is why it makes sense, in some circumstances, to create jobs.
2. encouraging consumption – during recessions economists often talk about a lack of consumer spending. In the long-run we might be concerned that people are spending too much or too little, for their own sake, but in the short-run consumer spending has another significance, as explained in the parable: if every farmer could be persuaded to some more vegetables at the market, then everyone would be better off, because they would be exchanging more. It is for this reason that Governments and central banks want to encourage consumer spending, though these reasons apply only during a recession.
3. bad news causing unemployment – when we talk about why there is unemployment we often accept that it can be caused by a negative event: e.g. by a fall in the stock market or house prices, because of the hurricane, or caused by a recession in another country. However this explanation is very superficial: why should bad news cause us all to work less? Think about the analogy of a single farm: if something bad happens to a farmer (a barn burns down, or the price of his crops falls), then why would the farmer work less? In most cases it seems more plausible that they will work more. Yet looking at history we do see that unemployment in a country often follows bad news. This connection can be explained by the model of sticky prices: if bad news causes people to spend less money, and if the price level doesn’t adjust immediately, then the amount of exchange will fall, and there will be less employment. And indeed, in this parable, in the long-run bad news will often cause people to work more.
Monetary policy: In real life monetary policy does not consist of just giving away money. Instead the central bank usually buys things with the newly created money. Generally they buy Government-issued bonds, and for this reason monetary policy is often described as raising or lowering interest rates, instead of as increasing or decreasing the amount of money, but the two actions are equivalent: when the central bank issues more money they use it to buy government bonds, buying bonds raises their price, which is the same thing as lowering the interest rate on those bonds (and in lowering the interest rate on government debt, in turn this tends to lower the interest rate on all debt). In the model of the farmers you could say this: the mayor stands by the gate on Saturday morning, and offers to lend each farmer 10 shells, which they must pay back next week, at some interest rate. The farmers are happy to take extra shells, if the interest rate is sufficiently low, and then because they now have more shells on hand, they will become relatively more inclined to spend shells, and this will tend to push the economy back towards greater exchange.⁸
Sticky inflation & downward nominal rigidities: Since the rise in unemployment in 2007 and 2008, many countries have had high unemployment stay high for a long time, yet inflation has not fallen as would be predicted by the Phillips curve. We would normally expect the high unemployment to reflect low demand, and therefore falling prices.⁹ A common explanation is that this is due to prices and wages (especially wages) being particularly slow to drop in nominal terms. I.e., people are very resistant to selling their goods, or their labour, at a lower nominal price than they had previously been selling it. There is strong evidence for this effect in the labour market, in the high density of zero-change in wages. ¹⁰
Taxation: For the mayor to raise money to pay for public services she has to impose a tax. She can either demand that each farmer pay a certain amount of money (a poll tax), or she can demand that they pay an amount proportional to the value of the vegetables they sell or buy (an income tax, or a consumption tax). If she uses an income tax then, from each farmer’s point of view, exchange is now less attractive: if the tax is 50% then, for every sack of carrots that I grow, I will receive only half a sack of cabbages, or half a sack of lettuces, etc.. So now each farmer will tend to do relatively less exchange, and become relatively more self sufficient.¹¹
This effect of taxes can readily be seen in everyday life: suppose that I would be happy to pay someone $10 to make me a sandwich at lunchtime, and there is someone who would be happy to work making sandwiches if they can sell them for $10. However every time that we make this transaction we have to set aside $3 for the tax collector. This discouragement will tend to decrease the amount of exchange done, so that I may make my own sandwiches in the morning, and the sandwich-maker stays at home instead. In this way higher taxes tend to lower the overall extent of specialization and exchange.
Price Setting. In the story I did not specify how prices are set, and in the model I assumed that prices are set competitively. This implies that each farmer has an enormous incentive to change their prices. Instead it may be more reasonable to think that they set their prices monopolistically, so that a small change in price has a small effect on sales.¹² Think about what this implies for the village: each farmer now has an incentive to raise their price above the competitive level, therefore the extent of exchange will shrink. The carrot farmer’s family will tend to eat somewhat more carrots than everyone else, and the beef farmer’s family will eat relatively more steak; i.e., the effect of monopoly is to retard trade and have a less efficient distribution of goods.¹³ Now consider the effect of prices being temporarily above their equilibrium level: sellers will only have a weak incentive to cut prices, because although a cut will increase sales, profits will not be much affected in the neighborhood of the optimum.¹⁴
Second, suppose that everyone else’s price is stuck at the old level, but you have the chance to adjust your price to reflect new conditions. Will you adjust it to the new equilibrium price? If you are in partial competition with other firms, then you only need to lower your price a little to bring in many more customers (i.e., prices are strategic complements). This fact is another reason that prices may adjust very slowly to their new equilibrium levels.
Why have money at all? Why don’t the farmers just barter instead? The usual argument for the existence of money is that it allows us to make indirect trades: suppose the potato farmer wants beans, the bean farmer wants garlic, and the garlic farmer wants potatoes. No pair of these farmers can make an exchange which directly makes both of them better off, they have to barter and accumulate vegetables that they will use later to exchange for vegetables that they want. However if we introduce money then each can directly make a trade, without accumulating goods that they would only want to resell later. In the model I described above barter would in fact work, this is due to the assumption that the situation is perfectly symmetric: in general barter is much less efficient than using money.
International effects: Suppose there are two villages, one which uses shells, one which uses pebbles. We assume that prices are slow to adjust in both villages, but that the exchange rate between shells and pebbles can adjust immediately, and also that trade is balanced in the long-run. Suppose extra shells are handed out. It then becomes relatively less attractive to hold shells due to expected inflation, so citizens of both villages will be less inclined to hold shells, causing more shell-expenditure, and lowering the value of shells relative to stones (the exchange rate). Thus expenditure in the pebble village will also decrease because it has become relatively more attractive to buy shell-denominated goods. Thus expansionary monetary policy in one country tends to lower expenditure in other countries; but expansionary fiscal policy in one country will tend to raise expenditure in other countries.
Monetary union: Suppose there are two villages with the same currency, but a fall in demand occurs in only one of them. In this case monetary policy cannot be as effective in counteracting the fluctuations in demand, because stimulating the depressed village has the side-effect of over-stimulating the other village.
Debt-deflation: In general the model implies that when there is a recession it would be best if all wages and prices could fall. However a change in prices could also have a second effect: if the farmers have been lending money between themselves, then a fall in the price level will make the lenders richer, and the borrowers poorer. (...)¹⁵
Stagflation and expectations. As discussed above, the basic theory predicts that booms will be times of high inflation, and recessions will be times of low inflation. In the 1970s and early 80s many countries experienced “stagflation”: high inflation and high unemployment at the same time. A common diagnosis is that in the early 1970s many central banks increased their money supply, to boost employment and output. If their output had been below the natural level, this would have kept prices constant. However output was not below its natural level (or, alternatively, too much money was introduced due to political pressure). Thus the extra money caused inflation. As this continued for some time consumers and firms came to expect inflation, so that the natural level of output could only be achieved if prices kept rising at the same rate. In the early 1980s, having diagnosed the problem in this way, central banks cut the rate of growth of money supply – which was the equivalent of cutting the money supply in the world without inflation. This caused spending to fall (relative to expectations), and so prices were stuck at a higher than natural level, and so GDP fell.

⁸ Note that the farmers should be glad to borrow the shells at a positive interest rate because they get utility directly from holding the money.

⁹ Or, if inflation is sticky, then a fall in the inflation rate, i.e. disinflation.

¹⁰ Note that this argument only makes sense for sticky inflation, not for sticky prices. See for example Fuhrer, Olivei and Tootell (2011), and an IMF paper on disinflations during persistent large output gaps.

¹¹ In fact, in the perfectly symmetric framework here, an increase in taxes will increase exchange, because farmers have to sell more vegetables to pay the tax, but the volume of exchange will nevertheless be lower than the efficient level (which would be achieved with a lump sum tax).

¹² Blanchard & Kiyotaki (1987, AER) “Monopolistic Competition and the Effects of Aggregate Demand”

¹³ The effect of monopoly power is clear in everyday life. Suppose that everything was priced at its marginal cost: software and music would be free, branded computers would be sold for the price of no-name computers, and shops in the middle of the cities would sell things for the same price you would pay way out on the outskirts of town.

¹⁴ In other words, the welfare loss is first-order, but the gains from changing prices are second-order.

¹⁵ See Krugman & Eggertson (2010) “Debt, Deleveraging & the Liquidity Trap.”

Citation

BibTeX citation:

@online{cunningham2025,
  author = {Cunningham, Tom},
  title = {Ten {Farmers} {Model} of {Macroeconomics}},
  date = {2025-04-12},
  url = {tecunningham.github.io/posts/2025-04-12-macro-farmers-parable.html},
  langid = {en}
}

For attribution, please cite this work as:

Cunningham, Tom. 2025. “Ten Farmers Model of Macroeconomics.” April 12, 2025. tecunningham.github.io/posts/2025-04-12-macro-farmers-parable.html.