Coordination Failures and Keynesian Intuition.

Macroeconomic models with demand-determined output are usually built on the assumption that goods (or labour) markets do not clear because prices (or wages) do not instantly adjust in response to various shocks. But the same basic Keynesian intuition – emphasizing the possibility of low-activity equilibria and multiplier effects – can also be generated in models in which there is no wage/price rigidity at all. This usually relies on the presence of what are called “coordination failures”. The previous question hinted at this issue. Let’s develop the idea a little more. The basic setting Suppose that individuals produce a good but must trade with others before they can consume. This assumption captures the reality in modern economies that most individuals specialize in the production of one product but consume a wide variety of products – thus trade is crucial to their prosperity. Specifically, suppose that any individual i’s current production, qit, depends positively on the probability that he or she will be able to make a trade, tit: qit = f(tit) : with f(0) = 0 and f(1) = q* Further, suppose that the probability of any individual making a trade depends positively on the level of aggregate output: tit = g(Qt) : where g(0) = 0 and g(q*) = 1 and Qt is simply the economy-wide average of all the values of qit Finally, we add a few technical assumptions just to make life simple: A1. There are so many individuals in this economy that each individual takes Qt as given, independent of their own value of qit. A2. The functions f and g are strictly increasing (and thus have strictly positive first derivatives). A3. Both f and g are strictly concave (and thus have strictly negative second derivatives). A4. Each individual’s utility is equal to his or her consumption, which equals production in the case of a successful trade and equals zero in the absence of a trade.

The questions:

a) Explain intuitively why any individual’s output is a positive function of other people’s (or aggregate) output.

b) Draw a diagram showing the function qit(Qt) (with Qt on the horizontal axis and qit on the vertical axis). What do you know about the shape of qit(Qt)? Explain.

c) We define an equilibrium to be a situation in which no individual wants to change his or her output given the output of all other individuals (this is precisely a “Nash equilibrium”). Identify in your diagram the one (or more?) Nash equilibria in this model. For simplicity, assume that all individuals are identical.

d) If you found more than one Nash equilibrium in part (c), is one equilibrium better than another? Explain.

e) What is the “coordination failure” is in this model? Explain.

f) Do you think there is a role for some “coordinating body” to help engineer a better equilibrium outcome? Explain what such a body might do to improve everyone’s utility – be creative!

g) Now consider changing assumption A3 so that the model can generate several equilibria. Explain what assumption would do this, and show this possibility in your diagram.

h) Now go back to a very basic Keynesian macro setting (as in a simple IS-LM model) in which the level of economic activity is “stuck” below the economy’s potential level. Think about firms’ desire to hire more workers and to produce more output, and also about individuals’ desire to work more and to purchase more goods and services. Do you see a “coordination problem” here? Explain.