There's a fine line between minimalism and unfurnished. I'm trying to find where that line is. [This is a heavily revised version of an old post.]
Simplicity and minimalism tend to go together, but they are not the same thing.
A simple model is one that is easy to understand. Which is a good enough reason for building a simple model.
A minimalist model is one that deliberately gets rid of everything that is not absolutely essential. The whole point of building a minimalist model is not just to make it easy to understand, but to try to figure out what is and what is not absolutely essential to understanding the phenomenon in question. If you have a successful minimalist model, you should be able to add in the stuff it leaves out and add more details to the story without changing the underlying plot. Everything else is embroidery.
Here is some of the stuff my minimalist model of recessions leaves out:
It is a general equilibrium model, but not a dynamic stochastic general equilibrium model. It leaves out time and uncertainty. It's a one-period model, with certainty.
Because it is a one period model, it leaves out saving and investment, borrowing and lending, and interest rates.
It leaves out production and employment. It is a pure endowment economy. Depending on precisely how you define "GDP", GDP is either fixed exogenously, or else zero.
So if you think time and uncertainty, saving investment and interest rates, fluctuations in output and employment, are essential to understanding recessions, my model says you are wrong. My model says those are optional details, that you can add in if you wish, that do not change the underlying plot of the story. They are just embroidery.
My model is a general equilibrium model of monetary exchange, with one sticky price (the price of money). Those are the things I think are essential.
There are three consumption goods: call them apples, bananas, and mangoes. You need exactly three goods in a minimalist model of recessions. Four is too many, and two is not enough.
All agents have the same preferences U = log(Ca) + log(Cb) + log(Cm)
Half the agents (the alphas) have an endowment of 200 apples and 100 mangoes each. The other half (the betas) have an endowment of 200 bananas and 100 mangoes each.
Let mangoes be the numeraire. Assume the price of apples is always equal to the price of bananas, and call that price P. So 1/P is the price of mangoes in terms of apples or bananas. Assume P is sticky.
In market-clearing competitive equilibrium P=1. Each alpha and beta swap 100 apples for 100 bananas. Each agent consumes 100 of each of the three fruits. That's also the social optimum, for a utilitarian central planner.
If P > 1 there is an excess demand for mangoes and an excess supply of apples and bananas. But this disequilibrium price has zero effect on the allocation of goods. Each alpha and beta still swap 100 apples for 100 bananas. Each agent still consumes 100 of each of the three fruits.
If P < 1 there is an excess supply of mangoes and an excess demand for apples and bananas. But this disequilibrium price has zero effect on the allocation of goods. Each alpha and beta still swap 100 apples for 100 bananas. Each agent still consumes 100 of each of the three fruits.
The reason the sticky price of mangoes in terms of apples or bananas has zero effect on the allocation of goods is because at the market-clearing price P=1 there is no trade in mangoes anyway. The only trade is between apples and bananas, and I have assumed the relative price of apples to bananas is always at the equilibrium relative price, so alphas and betas will always trade the optimal number of apples and bananas.
Now assume that mangoes are used as the medium of exchange. This means there is a market in which mangoes are traded for apples (the "apple market"), and a market in which mangoes are traded for bananas (the "banana market"), but no market in which apples are traded for bananas directly. The reason is that mangoes are portable, but apples and bananas must be eaten directly off the tree, or they taste bad, and agents are anonymous so can't swap IOUs for apples or bananas. So the only way agents can trade apples and bananas is by using mangoes as the medium of exchange.
If P = 1 the allocation is exactly the same as in barter. The alphas carry mangoes to the betas, buy bananas with mangoes, and eat those bananas on the spot. The betas carry mangoes to the alphas, buy apples with mangoes, and eat those apples on the spot. Each agent consumes 100 of each fruit.
If P > 1 we get a recession. There is an excess supply of apples in the apple market, so the alphas won't be able to sell as many apples as they want. There is an excess supply of bananas in the banana market, so the betas won't be able to sell as many bananas as they want. It is the betas who decide how many apples to buy, and how many apples the alphas can actually sell. It is the alphas who decide how many bananas to buy, and how many bananas the betas can actually sell. Alphas maximises utility taking into account the constraint on how many apples they can actually sell. Betas maximise utility taking into account the constraint on how many bananas they can actually sell.
Let A be the number of apples sold per agent, and let B be the number of bananas sold per agent.
In the banana market, alphas choose B to maximise U = log(200-A) + log(B) + log(100+PA-PB) taking A as given.
In the apple market, betas choose A to maximise U = log(A) + log(200-B) + log(100-PA+PB) taking B as given.
The alpha's first order condition gives us the constrained demand function for bananas:
Bd = 0.5(100/P + A)
The beta's first order condition gives us the constrained demand function for apples:
Ad = 0.5(100/P + B)
[If you are feeling Old Keynesian, you can add the monetary demands for apples and bananas together to get the desired Aggregate Expenditure function: (A+B)d = 0.5(200/P + (A+B)) and interpret (A+B)d as desired Aggregate Expenditure, (A+B) as National Income, and 0.5 as the marginal propensity to consume.]
Solving for the Nash Equilibrium gives us:
A = B = 100/P (for P > 1) [I could re-write it as A = B = M/P where M is the endowment of mangoes.]
This minimalist model of recessions gives us a very simple message: recessions are a reduction in the volume of monetary exchange caused by an excess demand for the medium of exchange. Recessions reduce utility because some mutually advantageous exchanges do not take place.
[For completeness, we can solve the model for P < 1, where there is excess demand for apples and bananas, so it is buyers of apples and bananas who are constrained in how much they can buy. The Nash Equilibrium is A = B = 200 - 100/P ]
Does it really matter that this model leaves a lot of things out?
It would be easy to add output and employment to the model. Replace "apples" with "labour of hairdressers", and "bananas" with "labour of manicurists". People produce services for sale with some of their labour, and consume the rest of their labour as leisure. In a recession output and employment falls, and workers are consuming more leisure than they want to. But it's exactly the same model.
It would be easy to add borrowing and lending to the model, by making it multi-period. We could solve for the rate of interest. But nobody would want to borrow or lend in equilibrium anyway. It's exactly the same model.
We could make mangoes a durable good, that never depreciate, and never get eaten, but you need to carry a stock of mangoes from one period to the next, because you might get hungry at the beginning of the period and want to buy bananas before you have sold any apples. The direct utility from consuming mangoes gets replaced by the indirect utility of being able to buy and consume bananas or apples whenever you feel like it. It's (almost) exactly the same model.
We could have a central bank create paper mangoes, and even pay or charge interest on those holding paper mangoes. Or electronic mango accounts, that could have either a positive or negative balance. It's (almost) exactly the same model.
Recessions are not about output and employment and saving and investment and borrowing and lending and interest rates and time and uncertainty. The only essential things are a decline in monetary exchange caused by an excess demand for the medium of exchange. Everything else is just embroidery.