Teaching

Oil Price Lesson Plan for Economic Principles

Joy BuchananLeave a comment

Alex Tabarrok noted in Oil versus Ice Cream that he and Tyler, as textbook authors, “chose the oil market as our central example. Oil is always in the news…”

when a student sees that the price of crude has surged past $100 a barrel because Iran closed the Strait of Hormuz—choking off 20% of the world’s oil supply—they have the framework to understand what is happening. Supply shock, inelastic demand, expectations and speculation, the macroeconomic transmission to GDP—it’s all right there in the headlines.

In a classroom, a good way to begin is to ask the students to tell you what they have noticed recently about oil or gas prices. Having the students obtain the oil price data themselves could be fun, if you are in an environment with screens/computers.

A data source for undergrads is the FRED chart for WTI crude oil prices. It is clean and easy to explain in class. An instructor with slides could pull this up in real time. https://fred.stlouisfed.org/series/DCOILWTICO

Ask students: “Is this price change primarily explained by

  1. Increase in demand
  2. Decrease in demand
  3. Increase in supply
  4. Decrease in supply

Correct answer: d. Decrease in supply

If you cover elasticity, this is especially helpful as an example. “Why would the price jump more when demand is inelastic?”

It’s not too late to work this into a lesson plan for the Spring 2026 semester, economic teachers. I might use it to illustrate supply shocks next week.

This event is a classic example of a negative supply shock: a disruption in the Strait of Hormuz would reduce the amount of oil reaching world markets, pushing energy prices sharply upward. Because oil is an important input for transportation, manufacturing, and heating, higher oil prices raise costs across much of the economy. Firms may cut production, households may spend more on gasoline and utilities and less on other goods, and overall economic activity can slow. That is why economists worry that large oil supply shocks can contribute to recessions. They do not just make one product more expensive; they can ripple outward, reducing real income, lowering consumer confidence, and weakening GDP growth while inflation rises.

Related posts. The whole crew showed up this month:

James from March 12: Is a US Oil Export Ban Coming?

Jeremy from March 18: Gasoline Prices Have Increased at Record Rates, but Remain At About Average Levels of Affordability

Tyler from March 22: How much more will oil prices have to go up?

MattY from March 24: Why hasn’t oil gotten even more expensive?

Austin Vernon: https://www.austinvernon.site/blog/thestrait.html

Cournot & Stackelberg Math

Zachary BartschLeave a comment

This post solves for the equilibrium quantity of production with quadratic total cost under Cournot and Stackelberg competition.

Say that there are two firms. They produce the exact same quality and type of goods and sell them at the same price. Let’s also assume that the market clears at one price. Finally, let’s assume increasing marginal costs.

Let’s say that they face the following demand curve:

The firms have a total cost of:

The marginal cost is the derivative with respect to the choice variable for each firm, or their respective quantities produced:

The total revenue is just the price times the quantity sold.

This is all standard fare for economic modeling. You’re free to make different assumptions. You can even adopt different slopes in the demand curve to reflect goods with different characteristics.

Cournot Competition

If you imagine a lengthy production process, or otherwise that they physically attend the same market, then it’s reasonable to assume that they don’t know one another’s choice of quantity produced.

We know how firms maximize profit: They produce the quantity at which the marginal revenue equals the marginal cost. But, what is marginal revenue? The derivative of total revenue with respect to the choice variable:

Now we can set the marginal revenue equal to marginal cost and solve for the optimal level of output:

Notice that the optimal level of output depends on the production decision of the other firm. These are called response functions. If we solve for the quantities at which they intersect, then we are solving for where both firms are producing the best response to one another. This is known as a Pure Strategy Nash Equilibrium (PSNE).

Luckily, in many applications, one or more of the above terms are zeros, which makes things much simpler.

The general process for solving for the Cournot equilibrium is:

  1. Set MR=MC to find the response functions.
  2. Find where the response functions intersect.

Stackelberg Competition

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The Economic Story of Mike Mulligan and His Steam Shovel

Zachary Bartsch1 Comment

Mike Mulligan and His Steam Shovel, by Virginia Lee Burton, is a classic 1939 children’s book about a man, Mike Mulligan, and his beloved steam shovel, Mary Anne, who are replaced by modern machinery. They get one last chance to demonstrate their worth by digging the cellar for a new town hall in a single day.

This book is more than just a nostalgic children’s story with a happy ending. This is a tale about economic history, comparative advantage, non-pecuniary benefits, labor and capital heterogeneity, and, of course, transaction costs.

Here’s some background. Historically, excavating or earth-moving equipment was powered by steam. Much like a steam engine locomotive (train), a steam shovel burns coal to heat water in a boiler, creating steam that can drive pistons that operate the mechanics. The result is machinery that can move a greater volume of soil at a faster speed than humans with simple hand shovels. Advancements in oil extraction and refining and internal combustion made the steam methods obsolete. Diesel or gasoline made earth movers safer, faster, and larger all because there was no need to build high pressures from boiling water. Steam pressure in the field takes a lot of time and is dangerous. 

Here is how the story goes. Mike enjoys his earth-moving work with his steam-shovel and is proud to be more productive than hand-shovels. One day, diesel, electric, and gasoline-powered shovels arrive. They’re bigger and better than Mary Anne. She is now obsolete. It’s unclear whether Mike’s skills are transferable to the newer equipment, but he implicitly prefers working with Mary Anne.  Together, they can’t compete in the urban areas where the value placed on quick excavation is high. So, they flee to the countryside.

The text doesn’t say why the newer shovels aren’t in the countryside. Let’s address that first. The new shovels haven’t spread to the rural areas because the opportunity cost is too high. Diesel Shovels are expensive and the owners/operators need revenue from many jobs in order to pay for their equipment in a reasonable amount of time and earn a positive return. Rural areas don’t have the same willingness to pay for as many projects, so less specialized capital is limited by the smaller extent of the market. Clearly, a higher cost of capital – the cost of the loan that pays for the diesel shovels or the alternative uses of the resources – accentuate the necessity for project volume.

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Telephone Classroom Game for Teaching Large Language Models

Joy Buchanan1 Comment
LLM_Telephone_Game_SheetDownload

Use the above game to generate interaction in a class setting. Students collectively form an LLM and have fun seeing the final sentence that gets produced. I call this game “LLM Telephone” based on the classic game of telephone. I suggest downloading the file LLM_Telephone_Game_Sheet and handing out printed copies. However, this game could be adapted to a virtual setting.

The nice thing about passing papers in the classroom is that you can have several sheets circulating in a quite room, so when the final sentence is read allowed it comes as a surprise to most people.

If you’d like to have a handout to follow the game with a more technical explanation, you can use this two-page PDF:

LLM_Telephone_Game_ExplainDownload

The game relies on a player presenting two tokens of which the next player can select their favorite. Participants should be bound by the rules of grammar and logic when making their selection and presenting two tokens to the next player.

This game works as a fun ice breaker for any type of class that touches on the topic of artificial intelligence. It is suitable for many ages and academic disciplines.

Macroeconomic Policy In a Nutshell

James BaileyLeave a comment

What I’m telling my Intro Macro students on the last day of class, since we weren’t able to get through every chapter in the textbook:

A few of you might end up working in economic policy, or in highly macro-sensitive businesses like finance. For you, I recommend taking followup classes like Intermediate Macroeconomics or Money and Banking so you can understand the details. For everyone else, here are the very basics:

  1. In the long run, economic growth is what matters most. The difference between 2% and 3% real GDP growth per capita sounds small in a given year, but over your lifetime it is the difference between your country becoming 5 times better off vs 10 times better off.
  2. How to increase long-run economic growth? This is complicated and mostly not driven by traditional macroeconomic policy, but rather by having good culture, institutions, microeconomic policy, and luck.
  3. In the shorter run, you want to avoid recessions and bursts of inflation.
  4. High inflation means too many dollars chasing too few goods. To fix it, the federal government and the central bank need to stop printing so much money (the details can get very complicated here, but if we’re talking moderately high inflation like 5% the solution is probably the central bank raising interest rates, and if we’re talking very high inflation like 50% the solution is probably a big cut to government spending).
  5. If there is a recession (which will look to you like a big sudden increase in layoffs and bankruptcies), the solution is probably to reverse everything in the previous point. The government should make money ‘easier’ via the central bank lowering interest rates while the federal government spends more and taxes less.
  6. If you don’t take more economics classes, you will likely hear about macro issues mainly through the news media and social media. You should be aware of their two main biases: negativity bias and political bias.
    • Negativity Bias: If It Bleeds, It Leads on the news. Partly this is because bad news tends to happen suddenly while good news happens slowly, so it doesn’t seem like news; partly it just seems to be what people want from the news and from social media.
    • Political Bias: People tend to seek out news and social media sources that match their current preferences. These sources can be misleading in consistent ways for ideological reasons, or in varying ways based on whether the political party they like is currently in power.
  7. There are different ways to measure each key macroeconomic variable. Think through them now and make a principled decision about which ones you think are the best measures, and track those. Otherwise, your media ecosystem will cherry-pick for you whichever measures currently make the economy look either the best or the worst, depending on what their biases or incentives dictate.
  8. There are good ways to keep learning about economics outside of formal courses and textbooks, I list a few here.

Visualizing the Sharpe Ratio

Zachary BartschLeave a comment

We all like high returns on our investments. We also like low volatility of those returns. Personally, I’d prefer to have a nice, steady 100% annual return year after year. But that is not the world we live in. Instead, there are a variety of returns with a diversity of volatilities. A general operating belief is that assets with higher returns tend to be associated with greater return volatility. The phrase ‘scared money don’t make money’ implies that higher returns are risky. The Sharpe ratio is a tool that helps us make sense of the risk-reward trade-off.

Let’s start with the definition.

By construction, the risk-free return is guaranteed over some time period and can be enjoyed without risk. Practically speaking, this is like holding a US treasury until maturity. We assume that the US government won’t default on its debt. Since there is no risk, the volatility of returns over the time period is zero.

Since an asset’s return doesn’t mean much in a vacuum, we subtract the risk-free return. The resulting ‘excess return’ or ‘risk premium’ tells us the return that’s associated with the risk of the asset. Clearly, it’s possible for this difference to be negative. That would be bad since assets bear a positive amount of risk and a negative excess return implies that there is no compensation for bearing that risk.

The standard deviation of an asset’s returns are a measure of risk. An asset might have a higher or lower value at sale or maturity. Since the future returns are unknown and can end up having any one of many values, this encapsulates the idea of risk. Risk can result in either higher or lower returns than average!

Putting all the pieces together, the excess return per risk is a measure of how much an asset compensates an investor for the riskiness of the returns. That’s the informational content of the Sharpe ratio, which we can calculate for each asset using historical information and forecasts. Once we’ve boiled down the risk and reward down to a single number, we can start to make comparisons across assets with a more critical eye.

Sometimes friends or students will discuss their great investment returns. They achieve the higher returns by adopting some amount of risk. That’s to be expected. But, invariably, they’ve adopted more risk than return! That means that their success is somewhat of a happy accident. The returns could easily have been much different, given the volatility that they bore.

Let’s get graphical.

Consider a graph in (standard deviation, return) space. In this space we can plot the ordered pair for some portfolios. The risk-free return occurs on the vertical intercept where the return is positive and the standard deviation is zero. Say that a student was thrilled with asset A’s 23.5% return and that it’s standard deviation of returns was 16%. Meanwhile, another student was happy with asset B’s 13.5% return and 5% standard deviation. With a risk-free rate of 3.5%, the Sharpe ratios are 1.25 & 2 respectively. We can plot the set of standard deviation and return pairs that would share the same constant Sharpe ratio (dotted lines). Solving for the asset return:

The above is simply a linear function relating the return and standard deviation. In particular, it says that for any constant Sharpe ratio, there is a linear relationship between possible asset returns and standard deviations. The below graph plots the two functions that are associated with the two asset Sharpe ratios. The line between the risk-free coordinate and the asset coordinate identifies all of the return-standard deviation combinations that share the same Sharpe ratio. This line is known as the iso-Sharpe Line.

With this tool in hand, we can better interpret the two student asset performances. There are a couple of ways to think about it. If asset A’s 23.5% return had been achieved with an asset that shared the Sharpe ratio of asset B, then it would have had risk that was associated with a standard deviation of only 10%. Similarly, if asset A’s volatility remained constant but enjoyed the returns of asset B’s Sharpe ratio, then its return would have been 35.5% rather than 23.5%. In short, a higher Sharpe ratio – and a steeper iso-Sharpe line – imply a bigger benefit for each unity of risk. The only problem is that a such an nice asset may not exist.

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Portfolio Efficient Frontier Parabolics

Zachary Bartsch5 Comments

Previously, I plotted the possible portfolio variances and returns that can result from different asset weights. I also plotted the efficient frontier, which is the set of possible portfolios that minimize the variance for each portfolio return.* In this post, I elaborate more on the efficient frontier (EF).

To begin, recall from the previous post the possible portfolio returns and variances.

From the above the definitions we can see that the portfolio return depends on the asset weights linearly and that the variance depends on the asset weights quadratically because the two w terms are multiplied. Since the portfolio return can be expressed as a function of the weights, this implies that the variance is also a quadratic function of returns. Therefore, every possible portfolio return-variance pair lies on a parabola. So, it follows that every pair along the efficient frontier also lies on a parabola. Not every pair lies on the same parabola, however – the efficient frontier can be composed on multiple parabolas!

I’ll use the same 3 possible assets from the previous post, below is the image denoting the possible pairs, the EF set, and the variance-minimizing point.

One way to find the EF is to calculate every possible portfolio variance-return pair and then note the greatest return at each variance. That’s a discrete iterative process and it definitely works. One drawback is that as the number of assets can increase the number of possible weight combinations to an intractable number that makes iterative calculations too time consuming. So, we can instead just calculate the frontier parabolas directly. Below is the equation for a frontier parabola and the corresponding graph.

Notice that the above efficient frontier doesn’t appear quite right. First, most obviously, the portion below the variance-minimizing return is inapplicable – I’ve left it to better illustrate the parabola. Near the variance-minimizing point, the frontier fits very nicely. But once the return increases beyond a certain level, the frontier departs from the set of possible portfolio pairs. What gives? The answer is that the parabola is unconstrained by the weights summing to zero. After all, a parabola exists at the entire domain, not just the ones that are feasible for a portfolio. The implication is that the blue curve that extends beyond the possible set includes negative weights for one or more of the assets. What to do?

As we deduced earlier, each pair corresponds to a parabola. So, we just need to find the other parabolas on the frontier. The parabola that we found above includes the covariance matrix of all three assets, even when their weights are negative. The remaining possible parabolas include the covariance matrices of each pair of assets, exhausting the non-singular asset portfolios. The result is a total of four parabolas, pictured below.

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Looking Ahead: Post-Powell Interest Rates

Zachary BartschLeave a comment

Jerome Powell’s term as Fed Chair ends in late May 2026. President Trump has said that he will nominate a new chair and the US senate will confirm them. It may take multiple nominations, but that’s the process. The new chair doesn’t govern monetary and interest rate policy all by their lonesome, however. They have to get most of the FOMC on board in order to make interest rate decisions. We all know that the president wants lower interest rates and there is uncertainty about the political independence of the next chair. What will actually happen once Jerome is out and his replacement is in?

The treasury markets can give us a hint. The yields on government debt tend to follow the federal funds rate closely (see below). So, we can use some simple logic to forecast the currently expected rates during the new Fed Chair’s first several months.

https://fred.stlouisfed.org/graph/?g=1NwVQ

Here’s the logic. As of October 16, the yield on the 6-month treasury was 3.79% and the yield on the 1-year treasury was 3.54%. If the market expectations are accurate, then holding the 1-year treasury to maturity should yield the same as the 6-month treasury purchased today and then another one purchased six months from now. The below diagram and equation provide the intuition and math.

Since the federal funds rate and US treasury yields closely track one another, we can deduce that the interest rates are expected to fall after 6 months. Specifically, rates will fall by the difference in the 6-month rates, or about 49.9 basis points (0.499%).  This cut is an expected value of course. Given that the cut is between a half and a zero percent, we can back out the market expectation of for a 0.5% vs 0.0% cut where α is the probability of the half-point cut.* Formally:

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Podcast on the Major Macro Events Since Y2K

Joy BuchananLeave a comment

The latest Macro Musings is an episode I could recommend to students in a macroeconomics class.

Jim Clouse on the Last 4 Decades at the Most Powerful Central Bank in the World

Since the great depression is over, what are the big events of the 21st century for macroeconomics?

9/11 and shoring up bank confidence subsequently

The Great Recession and preceding mortgage crisis

Covid and subsequent stimulus

This conversation is a tour of the trade offs under consideration at the Central Bank at these pivotal moments in the 21st century.

Beckworth: I think this is where it’s important to do the right counterfactual. What could have been could have been far worse, right? If there hadn’t been these interventions, so it’s easy to criticize from the outside, and there’s a lot of criticisms the Fed received at this time. Not to say we would have gone all the way to the Great Depression, but the fact that it was possible, right, this financial system was crashing. 

Does Trump Weaken the US Dollar?

Zachary Bartsch2 Comments

Talk to some economists and they’ll tell you that exchange rates aren’t economically important. They say that exchange rates between countries are a reflection of supply and demand for one another’s stuff. So, at the macro, it’s a result and not a determinant of transnational economic activity.

For individual firms at the micro level, it’s the opposite. They don’t affect the exchange rate by their lonesome and are instead affected by it. If you have operations in a foreign country, then sudden changes to the exchange rate can cause your costs to be much higher or lower than you had anticipated. The same is true when you sell in a foreign country, but for revenues. This type of risk is called ‘exchange rate risk’ since it’s possible that none of the prices in either country changed and yet your investment returns change merely because of an appreciated currency.

Supply & Demand

Exchange rates are determined by supply and demand for currencies. Demand is driven by what people can do with a currency. If a country’s goods become more attractive, then demand for those goods rise and demand for the currency rises. After all, most retailers and wholesalers in the US require that you pay using US dollars. Importantly,  it’s not just manufacturing goods that drive demand for currency. Demand for services, real estate, and financial assets can also affect the supply and demand for currency. In fact, many foreigners  are specifically interested in stocks, bonds, US treasuries, and other investments. The more attractive all of those things are, the more demand there is for them.

Of course, the market for currency also includes suppliers. Who does that? Answer: Anyone who holds dollars and might buy something. Indeed, all buyers of goods or financial products are suppliers of their medium of exchange. In the US, we pay in dollars. Especially since 1972, suppliers have also included other central banks and governments. They treat the US currency as if it’s a reserve of value, such as gold, that can be depended upon if they need a valuable asset (hence the name, “Federal Reserve”). This is where the term ‘reserve currency’ comes from – not from the dollar-denominated prices of some internationally traded commodities. Though, that’s come to be an adopted meaning.  

Another major supplier of currency is the US central bank. It has the advantage of being able to print US dollars. But it doesn’t have an exchange rate policy. So, it’s not targeting a particular price of the US dollar versus any other currency. The Fed does engage in some international reserve lending, but it’s not for the purpose of supplying currency to foreign exchange markets.  

The US Exchange Rate in 2025

One of the reasons that the US has such popular financial assets is that we have highly developed financial markets and the rule of law. People trust that, regardless of the individual performance of an asset, the rules of the game are mostly known and evenly applied. For example, we have a process to follow when bond issuers default. So, our popularity is not merely because our assets have higher returns. Rather, US investment returns have dependably avoided political risk – relative to other countries anyway.

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