Monetary Paradoxes of Baby-Sitting Cooperatives

The Global Financial Crisis of 2007 has led to a renewed interest in Keynesian theories. In particular, Krugman in “The Return of Depression Economics” argued that Keynesian ideas remain relevant to understanding 6196411489_a5cf9e16fc_bcontemporary recessions. To motivate this, he has used a real world example of the Capitol Hill Baby-Sitting Cooperative (BSC). According to an analysis by economists who were members of the Cooperative, the BSC suffered from a recession due to a shortage of “scrip”, the currency used to exchange baby-sitting services.

Krugman’s analysis is based on an intuitive and heuristic analysis by Sweeney and Sweeney (1977). However, the BSC is a very simple single good economy, where the sole function of money is to allow for inter-temporal trade. This simplicity allows for a rigorous analytic treatment. Our research was motivated by the idea of analytically validating the intuitive insights of the Sweeneys and Krugman. Is the BSC a Keynesian economy? Can a shortfall of money create a recession in this economy? A simple model which displays Keynesian effects should be useful in building understanding of these phenomenon in more complex situations.

A few authors who have analyzed the BSC economy have found Keynesian effects under the assumption of fixed prices. But in presence of fixed prices, the existence of an optimal quantity of money, and recession for low money is a triviality. The Keynesian rejection of neutrality of money is not based solely on sticky prices. In this paper, we create a simple model of the BSC economy to investigate the presence of Keynesian phenomena. The model leads to strange and paradoxical results, not available in earlier analyses. We list these results below.


  1. The BSC Economy has the Keynesian Beauty Contest That is, equilibria depend heavily on the beliefs of agents about how other agents will behave.
  2. The central question being investigated is: is money neutral in the BSC economy? This has a subtle, complex and perhaps paradoxical answer. In all models, money is “technically” neutral – that is, all levels of money are compatible with the same sets of equilibria. This is true even though prices are fixed. At the same time, money is not “expectationally” neutral. At any given level of money stock, coherent expectations about the value of money will be self-fulfilling. In our model, there are three possible coherent and self-fulfilling expectations about money: money is of high value, low value, or zero value.
  3. A paradoxical violation of Say’s Law: The BSC economy display several other phenomena which run counter to standard intuitions. Supply creates its own demand in two strong senses. In a single period, supply of baby-sitting is jointly produced with demand, and hence supply creates demand. In addition, all agents balance budgets across time, so that for any single agent, an act of supply is exactly matched by a demand for baby-sitting services at some other point of time. Despite this dual guaranteed match between supply and demand, some equilibria have excess supply, others have excess demand, and none have a match between supply and demand.
  4. Breakdown of Partial Equilibrium Supply and Demand Analysis. This phenomenon of mismatch between supply and demand has been noted by many authors, and attributed to the fixity of price – one scrip is worth one half-hour of babysitting. We show that flexible prices cannot resolve this problem. One might expect that the partial equilibrium (PE) Marshallian theory would work in a single good economy. However, we will see that supply and demand cannot be separated as required by PE analysis, and thus the intuitions generated by supply and demand analysis do not hold up.
  5. Excessive Trading is Possible. Intuition suggests that trade by mutual consent is always welfare improving, since both parties agree to the trade only under this circumstance. Thus, Kash et. al. argue that the volume of trade is a good indicator of welfare in the BSC economy. In our model, despite mutual consent, trades can be welfare decreasing, and banning certain trades can lead to welfare improvements. Equilibria with lower total trading volume can be superior to situations with higher trading volumes.

All of these paradoxical properties suggest that the surface simplicity of the BSC Economy is deceptive, and hides deep and murky complexities. Although it would be premature to jump to policy implications on the basis of such a simple model, these implications are valid for the BSC economy itself, and are radically different from those suggested by standard economic intuitions. Two of these implications are highlighted below:

  1. The value of money can change from high to low and to zero depending purely upon expectations in the BSC economy. It seems likely that this phenomenon will generalize far beyond the simple BSC economy, since multiple equilibria driven by expectations are ubiquitous in monetary models; see for example Evans and McGough (2005). Central Bank responses to speculative attacks on currencies are guided by the intuition that the value of currencies are determined by fundamentals. Thus, speculators cannot win if the fundamentals are sound. Many Central Banks have bet heavily and lost heavily against speculators on the basis of these intuitions. In the BSC economy, the value of money does not depend upon fundamentals, but purely on expectations about the value of money. Thus a speculative attack can succeed just by changing expectations, without any change in the fundamentals. A subtle and complex interaction between fundamentals and the value of money occurs because of the nature of expectations. If everyone believes that fundamentals are relevant to the value of money, then this becomes a self-fulfilling prophecy. Speculative attacks will then take the shape of news about change in fundamentals, regardless of whether or not such change has occurred or whether the changes being described in the news actually matter in the determination of the value of the currency. As long as the news convinces the public, and changes their expectations about the value, the attack will succeed, regardless of Central Bank interventions.  This matches empirically the way speculative attacks are conducted and has radical implications for policy in face of such attacks.
  2. The Sweeneys and Krugman suggests that low money supply leads to a recession in the BSC economy. In our model, this can happen but has radically different implications from the ones drawn by these authors. First, the expansion of money works through the expectations effect, and so monetary problems are not purely technical. They have a social dimension and work through consensus about the value of money. Second, even though increased money supply may increase the volume of trade, this may actually decrease social welfare. Thus, the so-called recession state, with low volume of trade and high value of money, may actually be superior in terms of welfare to a high volume of trade with low value of money. Again this is in strong conflict with standard economic intuitions.

An important lesson from our model is that choice of a particular equilibrium among a multiplicity of Nash Equilibria requires agents to coordinate plans.  The central message of Bicchieri (1997) is that we must go beyond individual rationality, and study how agents actually learn to resolve the coordination problem. Behavioral economics provides us with the possibility of studying such problems, involving how a particular Nash equilibrium is chosen. Duffy (2008) has provided an extensive survey of this literature. Our research suggests that we need to move beyond individual decision making to study collective decision making in problems with multiple Nash equilibria.

{Above is taken from Introduction; download full paper: Monetary Paradoxes of Babysitting Cooperatives}


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