Imagine: you run a wildly successful cake business, but you can only obtain milk by robbing the wealthiest man in the neighborhood. Business is booming, but he will kill you if he finds out. When do you stop?
In Kelly Reichardt’s First Cow (2019), King-Lu (Orion Lee) and Otis “Cookie” Figowitz (John Magaro) face this exact conundrum around optimizing output as they earn their fortune selling oily cakes in the Oregon frontier.
In the previous installments of this series, I discussed economic principles like diminishing marginal utility and the monopolistic practices of the pair’s oily cake business. As we turn our attention to the question of optimal output, we will examine the concepts of marginal cost-benefit analysis, expected value, and risk appetite to tease out an answer.
Economists like to think at the margin. In the output optimization problem, the incremental benefit from selling an additional unit of some product is called the marginal benefit, while the incremental cost of producing that additional unit is called the marginal cost. The optimal amount of production will always be the quantity at which the marginal cost of producing the last unit is equal to the marginal benefit of selling that unit.
Let us apply this framework to First Cow. King-Lu and Cookie steal milk every night from Chief Factor’s (Toby Jones) cow to make oily cakes. Each heist begets one cup of milk, each cup of milk makes a dozen cakes, and at 5 silver pieces per cake, a dozen cakes net them 60 silver pieces.
The marginal benefit of the heist, then, is the incremental satisfaction they feel from gaining an additional 60 silver pieces in sales. If we apply the law of diminishing marginal utility, we know that for each batch of cakes sold, their marginal benefit will decrease. Think of it this way: earning your first 60 silver peaces feels amazing, but when you have already accumulated hundreds, earning another 60 hardly feels like a game-changer.
On the other hand, the marginal cost increases as the risk of capture rises. Chief Factor notices early on that his cow produces little milk despite its immaculate pedigree. When he tries an oily cake for himself, King-Lu and Cookie become wary. He possesses a delicate palate, and given that he owns the only cow in Oregon, he could easily deduce that the pair have been stealing from him if he tastes the milk. To make matters worse, he “introduces” the pair to his prized animal only to find the cow displaying uncanny affection to Cookie.
“This is a dangerous game we’re playing here. Chief Factor has a delicate palate. He’ll taste his milk in there eventually.”
While the marginal benefit of making more money wanes, the marginal cost of stealing milk rises. Since the “costly” event may or may not occur, all we need to solve this problem is a methodology for valuing probabilistic outcomes. For this kind of question, economists created the concept of expected value.
Since many economic considerations must factor in uncertainty, economists multiply the value of an event by the probability of it happening to calculate the expected value of the event. If I flip a coin and give you $10 only if it lands “heads,” then the expected value of the coin flip is $10 x 0.5 = $5.
Let us apply this concept to King-Lu and Cookie’s question of how many more times they ought to milk the cow. We know that Chief Factor prefers draconian punishment—he suggests to the Captain that he should have killed his mutinous crew member instead of merely whipping him—so we can assume he will probably kill King-Lu and Cookie if he discovers that they have been milking his cow.
“Even a properly rendered death can be useful in the ultimate accounting.”
— Chief Factor
Since the probability of earning 60 silver pieces from a batch of oily cakes is 100%, the expected value of their marginal benefit is just the satisfaction of earning that silver. To calculate the expected value of marginal cost, however, they must multiply the loss of satisfaction from dying by the probability of being captured. If death costs, let’s say, 1,000,000 units of satisfaction, and there is a 1% chance of being caught, then the marginal cost of milking the cow has an expected value of 1,000,000 x 0.01, or 10,000.
We can thus prescribe the following: King-Lu and Cookie should stop milking the cow once the satisfaction of earning 60 more silver ingots no longer exceeds the expected cost of losing their lives.
It may seem morbid to perform this calculation, but Chief Factor points out, “Any question that cannot be calculated is not worth the asking.” Most decisions in life—even ones involving death—can be boiled down to a cost-benefit analysis that compares expected values where uncertainty is involved.
As it turns out, humans are complicated creatures in that we place an inherent value on risk itself. How we choose between outcomes involving uncertainty, then, depends on our individual appetites for risk.
Economists use the concept of risk appetite to gauge how much someone values certainty. Those who prefer guaranteed outcomes are called risk averse, while those who prefer to gamble are called risk seeking. Suppose, for example, you are offered two options.
Option A: I give you $5
Option B: I flip a coin and give you $10 if heads, $0 if tails
Perhaps you’d choose A because you’d rather take the guaranteed $5 than risk getting nothing, or perhaps you’d choose B because you’d rather gamble for $10 than only take $5. What makes this problem interesting is that the expected value for both outcomes is the same.
Expected value of A = 100% x $5 = $5
Expected value of B = 50% x $10 = $5
Since the monetary value of both options is equal, the decision maker’s choice is dependent on their risk appetite: those who choose A are more risk averse than the risk seekers who choose B.
Risk appetite plays a significant role in the dynamic between the risk averse Cookie and the risk seeking King-Lu. On numerous occasions, Cookie voices doubts about their secret milk heists, but King-Lu persuades him that the pay-out of selling more oily cakes is too profitable to pass up on. Consider, for example, when they first hatch the idea to sell the cakes: Cookie points out that the plan “seems dangerous,” and King-Lu states, “So is anything worth doing.” As he stands there with a confident, sly smile, we can see that he derives satisfaction from the thrill of taking risks.
In the end, there are ramifications that result from both of their differing risk appetites. King-Lu’s risk-seeking insistence on milking the cow more results in Chief Factor discovering their secret. Cookie’s risk averse inability to jump off the cliff to evade capture results in a presumably fatal head injury.
In their final moments, King-Lu and Cookie’s fate delivers an important reminder: economics merely provides an analytical framework to better understand certain questions, but it cannot always provide an easy answer. What is the probability a certain result occurs? What is its expected value in terms of cost and benefit? How does my innate appetite for risk sway my decision making in one direction or the other?
We cannot optimize every decision, but we can hold onto certain lessons. Next time you’re on a hot streak at the poker table, just remember—he who milks the First Cow should quit while he’s ahead.