Search in the goods market?

For economists

Imagine an economy made up of independent producers, who individually produce some good. Producers each have a fixed ‘capacity’ k of the output they produce. Producers are also consumers, but cannot consume their own good. Instead they search for other goods by visiting other producers. Agents as consumers have a certain demand for goods, which will depend on how much of their own good they sell, as well as some initial endowment of money and the price of goods in terms of money.

Traditionally we ignore the costs for consumers of visiting producers, and we assume that any visit will result in a purchase. As a result, for a given price level, we can have three situations. In the first, aggregate consumption demand is below aggregate capacity (the sum of all k), and producers end up with either unsold goods or idle capacity. In the second, aggregate demand is equal to supply. In the third, aggregate demand is above capacity. In this case we must have rationing of goods.

In this framework output is not always determined by aggregate demand, but only up to some limit. This is not how macroeconomic models typically work - they generally assume output is always equal to aggregate demand. The way New Keynesian models justify this is by assuming that producers can produce above ‘capacity’ (or that they prefer to always have some spare capacity), and that they will be happy to produce above capacity at a given price because they are monopolistic.

A recent paper by Pascal Michaillat and Emmanuel Saez applies the framework of search to the goods market. First, each visit by the consumer is costly (visiting costs) - some of the produced good is ‘lost’ (does not increase utility) as a result. So output (y, the sum of all trades) is greater than consumption (c) because of these visiting costs. Second, a visit may not lead to a trade. Whether it does depends on a matching function, which depends on the ‘tightness’ of the goods market = x, defined as the ratio of visits to capacity. Here is a diagram from their paper.

The consumption demand line is downward sloping, because a larger number of visits raises the effective price of the produced good. The output line is upward sloping, because more visits result in more trade, but the matching function is such that it gets steeper with more visits. However if visiting costs are linear in visits, that implies what the paper calls ‘consumption supply’ has this rather odd shape. (Think about the constant capital line in the Ramsey model.) For a given price, the intersection of the consumption demand and supply lines defines equilibrium tightness. Perhaps a simpler way of putting it is that consumers plan the number of visits they need to make given their consumption demand schedule.

Now shift the consumption demand line outwards, by reducing the price. (In a New Keynesian framework, think about the price as the real interest rate.) The line pivots about the x^m point, but output always stays below k. As tightness (number of visits) increases, more resources are used up in failed endeavours to make a trade, and consumption starts falling. Output is always ‘demand determined’, and there is no rationing.

It is still possible to think about different ‘regimes’, because the efficient level of tightness is where consumption is at a maximum. If tightness is below that point, we can say that demand is too low (the price level is too high), and vice versa.

Those familiar with matching models in the labour market will see the connections. Visits are equivalent to vacancies, for example. The key question is whether this transposition to the goods market makes sense, and what it achieves. To quote the authors: “casual observation suggests that a significant share of visits do not generate a trade. At a restaurant, a consumer sometimes need[s] to walk away because no tables are available or the queue is too long.” (What is it with economists and restaurants?!) We could add that this rarely means that consumption is rationed - instead the consumer attempts to make a similar trade at another restaurant. However this does have an opportunity cost, which this model captures.

In a subsequent post, I will look at their full model which has separate goods and labour markets, and the various types of unemployment that this can generate. Those that cannot wait can read their own account on Vox.