August 20, 2023

by Stephen Stofka

This week’s letter is about the formation of a price consensus between buyers and sellers. I’ll introduce a different perspective that might help us understand broad price changes. Visually oriented readers familiar with economics and statistics can listen to this letter and mentally picture these ideas as they walk the dog. However, I’ll present several graphs to illustrate the perspective.

Anyone who has taken an Economic course has been introduced to a supply demand diagram. Quantity is on the x-axis and Price is on the y-axis. The lines may be curved or straight. The intersection of the demand and supply lines is the equilibrium price, the long term average. A capitalist economy promotes change and the supply-demand diagram is a visual aid to understand how price and quantity respond to shifting conditions. Students learn how the supply-demand curves respond to changes in income, to better production technology, to price changes in other kinds of goods. That simple diagram demonstrates responses to government policies like taxes, transfer programs, price controls like apartment rents, and agricultural price supports.

The dotted line represents demand after a period of time, the one component missing from this 2-dimensional graph. While it pictures the formation of an equlibrium price it does not emphasize the broad price consensus that forms between buyers and sellers. To picture that let’s draw a probability distribution of sales at various prices and quantities. I’ll exchange the quantity and price axes so that price is on the horizontal x-axis and quantity is on the vertical y-axis.

I’ll redraw the chart, setting the average price to $0 with a short range of prices above and below that average. The equilibrium price is just the average long term price. The chart below highlights the narrow consensus over price between consumers (blue line) and suppliers (orange line). Rising prices induce more suppliers to enter the market. Declining prices attract more buyers. The supply and demand lines are curved, representing the number of sales taking place at each price level. The total number of units sold is 10,000.

Let’s consider a garden tool whose average price is $30. We will see some customers willing to pay $34, or $4 above that average price, but there are few of them. Likewise, there are few suppliers willing to sell at a price of $26, a price that is $4 below the average price.

To show price and quantity dynamics, the normal distribution graph is not as flexible or as simple as the conventional supply-demand diagram. The normal distribution chart can be viewed as a spread of prices over time, the third dimension. Just imagine that wedge of blue is a piece of pie so many weeks or months thick. Seeing price as a probability distribution does reflect a buyer’s reality in the sense that we prefer to shop with approximate prices in mind. Monthly surveys conducted by the BLS tell us that the prices of two categories – food and energy – are volatile, making it difficult for us to anchor a price expectation. These are the prices we encounter frequently when we fill up our cars, pay our utility bills and shop at the grocery store.

The graph is similar to a 2-dimensional triangle and is missing a critical component – time. The depth of a slice of pie can represent time periods. Demand operates on a shorter time scale than supply, an idea central to the analysis of Alfred Marshall, the economist who developed the supply-demand graph we use today. It’s a thinner wedge of pie.

Imagine that the average of a weekly tank of gas is $40. The blue pie of the normal distribution in the graph is sliced into a 100 vertical strips that statisticians call “bins.” Imagine that every one of those bins is a week and the center, the zero point, is an average of gas prices over two years. That is the time scale of demand. The time scale of supply is thicker, perhaps four times as long in some industries. The chart below shows the 2-year (demand) and 4-year (supply) averages of weekly gas prices for the past 25 years. Current 2-year average prices are at a historical peak. These prices are not adjusted for inflation. Adjusted for inflation, gas prices have declined in the past 40 years. After adjusting for fuel efficiency, gas prices are comparable to those in the 1950s.

The supply chain, including the banks that fund them, must look far into the future. Each one of the bins in the normal distribution chart could represent a month, not a week, forming an eight year average. No one could have foreseen a pandemic that interrupted global production. Coming out of the pandemic, businesses responded to low interest rates and anticipated a surge in demand. In an 18-month period from the fall of 2020 to the spring of 2022, private investment increased by 22%. The inflation that erupted in the spring of 2022 was a combination of growth in short term demand and long term supply investment. As soon as the Fed began raising interest rates, the surge in private investment ended and leveled out.

The normal distribution chart helps us see price as a probability distribution dispersed over time. Any chart that reminds us of pie is a useful and welcome analytical tool.

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Photo by Michael Dziedzic on Unsplash

Keywords: probability distribution, supply, demand, price