Marginal Losses

April 23, 2023

by Stephen Stofka

Today’s letter is about marginal loss and marginal value. We are going to take a rollercoaster ride from Einstein to relationships to the Bible to the marginalist revolution in late 19th century economics. Buckle in.

Einstein’s formula equating mass and energy confused me for a time. With all the mass in the universe, it seemed that it would blow itself up. At some point I read that the m in E = mc2 represented the mass lost and a light bulb turned on in my young head. A grain of sugar lost from a sugar cube weighed almost nothing but when multiplied by c2well, no wonder the atom bomb was so powerful.

We understand the value of a partner when we lose them. The worst part of breaking up with someone is thinking that they experience the loss far less than we do. We think back and wonder if we valued them more than they valued us throughout the relationship. The pain of loss becomes the yardstick that we measure the parts of the relationship. After the death of a dog, we remember them licking us awake in the morning with far more fondness than we actually felt when we just wanted a few more minutes of sleep rather than a walk in the cold morning air.

In the Parable of the Workers in the Vineyard, the workers hired early in the day get the same daily pay as those hired later in the day. Those who worked least, i.e. the last workers hired in the day, became the standard by which all the workers’ pay was evaluated. That became their standard of value. By this measure, the landowner had cheated the workers hired earlier in the day. In the landowners valuation, the workers were indistinguishable. To each worker, they distinguished themselves by the amount of time spent working and discomfort endured.

In a market stall in a developing country, the produce sold by each vendor may be largely indistinguishable. The value of what each vendor sells is mostly determined by what would happen if they weren’t there, not by the amount of effort they put into growing and harvesting what they offer for sale. Is that fair?

John Bates Clark was a leading economist of the late 19th and early 20th century who asked that very question. In Chapter 7 of The Distribution of Wealth he noted that the price of all the wheat grown by farmers in the northwest United States was determined by the price of whatever surplus wheat there might be when all the wheat reached the marketplace. This price was fixed on a London exchange thousands of miles away. Why should the marginal surplus determine the price of an entire crop?

A pound of ground beef might sell for $5. Add 10 cents worth of spices, 20 cents of packaging, 50 cents of labor and that same product now sells for $8 as Italian meatballs. Why do the marginal ingredients determine the price of the entire pound of ground beef?

In Chapter 8, Clark noted that a worker’s value to an employer is not their marginal product – not directly. It’s the loss to the employer if a worker left, or the marginal loss. Clark called it a zone of indifference. Within that zone are the expendable workers. Should those expendable workers become the standard of value just as in the parable of the vineyard? These are uncomfortable conversations. Workers have families. They contribute more to the community than their marginal worth to an employer. They take their kids to soccer games and coach Little League games. They volunteer at food banks, animal shelters and museums. How should society pay for that worth?

Clark published his book The Distribution of Wealth in 1899 when employers provided few benefits or protections for workers and factories were crowded with child workers. There was no income tax. In the U.S. today, employers are required to pay some part of society’s share of a worker’s worth to the community. The employer then includes those societal costs in the price of their product and the burden is shared among the employer’s customers (note below).

This is an indirect or hidden tax, a more politically feasible type of taxation. We judge our taxes at the margin – the amount that we have to give to the government on the last dollar we earn. The press cites marginal tax rates, the rate on the last dollar, and not the effective tax rate, the total amount of tax divided by our total income. We might be in the “25% tax bracket” when our effective rate is only 11%. We are guided by marginal loss thinking.

Repeated experiments have demonstrated that we assign a greater value to marginal losses than we do marginal gains. Consider this, a variation of Einstein’s thought experiment with moving trains. Consider two observers – John is on a moving train and Mary is an omniscient observer on a train platform. In this case, the moving train is time. John has a $100, which becomes his standard of value. Then some event happens before the next stop and John has $105, which becomes his new standard of value. Like the rest of us, John forms expectations of the future based on his current motion. He expects a gain of about $5 before the subsequent stop. But something happens and John loses $5. From Mary’s point of view, John has the same amount of money he started with. But John feels like he has lost $10, the initial gain and the expected gain that he did not receive.

No one has to teach us marginal loss thinking. It seems to be instinctual because we live at the margin, breathing in and out every minute of our lives. The very act of breathing creates a loss of pressure in our lungs. Sometimes marginal thinking is appropriate and sometimes thinking at the average is more appropriate. As investors, not traders, we must think at the average, not the margin, to survive.


Photo by Roman Fox on Unsplash

*These societal costs are not the Marginal Social Costs (MSC) referred to in Environmental Economics texts. Those are costs that an employer imposes on society.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s