The cache is NOT at the posted coordinates! Solve the puzzle below to figure out where the cache is located.
For the past 16 years that I've been employed in the Social Studies Department at Altoona Area High School, I've taught almost exclusively government & civics classes. Occasionally, I've taught classes on global politics as well. After all, one could say that I have a comparative advantage in using my political science background to teach those kind of classes to our students.
Fast forward to this school year: I found out five days before the school year started that I was going to be teaching college-level (AP) Microeconomics and Macroeconomics. GULP! It's been a looooooooooonnng time since I took either Micro or Macro in my undergrad days. I'm slowly adjusting to what is essentially a math course with some social studies concepts sprinkled in. It's been fun so far, albeit very different than those civics/government classes that I still also teach.
One thing's for sure: economics definitely makes for more interesting geocaching puzzles than government does. So here's a fairly difficult one for you. Everything you need to complete the "lesson" is provided below:
The Elasticity of Demand:
In our previous lesson, we looked at the concept of supply and demand. Remember that the Law of Demand states that there is an inverse relation between the price of a good and a person's demand for it. In other words, people are willing to buy more and more of an item's quantity the lower the price is.
But what if there was a way to measure how responsive that demand is to price changes? There is! We call it the elasticity of demand. We can classify all demand into essentially two categories: elastic demand and inelastic demand.
Let's start with inelastic demand. This would refer to items for which a rise in price will not really change demand too much. Gasoline is the classic example: we need gasoline to power many of our vehicles; therefore, we're willing to continue to buy it even if the price goes up another $0.25/gallon. Many types of prescription medication are inelastic for the same reason. Utilities, such as electricity and natural gas are another example. Demand is relatively inelastic for cigarettes, as are narcotics in the illegal drug market. You get the idea.
On the other hand, elastic demand IS very sensitive to price changes. Common examples include luxury goods, airline tickets, or items for which there are many subsitutes. Another example of elastic demand is that for fast food. No doubt, we've seen various fast food restaurant chains grapple will declining demand amid price inflationary price increases. The more elastic the demand is, the less willing people are to pay at higher prices.
Using a supply and demand graph, we can represent various elasticies visually. Essentially, the steeper the slope, the more inelastic the demand is. In the diagram above, D1 has a far steeper slope than D2. There's much more variation along the X axis for D2, because the demand is heavily responsive to a price increase. D1, on the other hand, does not move as much along the X axis as the price increases. Therefore, D1 represents a more inleastic demand than D2 does.
Calculating Demand Elasticity Coefficients:
Economists can also determine how elastic a demand is by assigning a coefficient to the situation's change in prices over time. This is done by calculating the change in the quantity demanded over time, divided by the change in the price over time. As an equation, we can represent this as:
Once a coefficient is determined, we can determine its elasticity by using the following rules:
- Elastic demand is anything with a coefficient > 1
- Inelastic demand is anything with a coefficient < 1
So how do we calculate these changes? I prefer the midpoint formula, so that's what we're going with.
Let's practice this with a little word problem. Let's say a bakery is selling cupcakes at $20/dozen and sells 3,000 cupcakes throughout September. Then, next month, the bakery lowers their price to $15/dozen and sells 4,500 cupcakes throughout the month October.
We can plug in these numbers to yield the following equation:
Because the absolute value of that coefficient comes out to 1.4, we know that the demand for cupcakes is elastic, and therefore sensitive to price changes.
Test Question:
Now it's your turn!
As you know, geocaching offers a subscription service for its premium membership. Currently, it's $39.99/year. Let's just make the math easier and say they're currently charging $40/year. Currently, there are about 800,000 active premium members worldwide.
However, let's pretend that HQ decides to raise the premium membership rate to $45.99/year ($46) starting in 2026. Estimates from the analytics department at HQ predict that the number of premium memberships in 2026 with this price change will be around 740,000.
Your task is to determine whether the demand for premium memberships in this scenario is elastic or inelastic. To do this, calculate the coefficient of elasticity. Once you have the coefficient, round your decimal the nearest hundredth. Plug that into the Certitude checker and you will have the coordinates to this cache.
You can validate your puzzle solution with
certitude.
Note: there's one cache left in this AP Micro series: the HARDEST version. Hope you remember some basic geometry from high school! It should be out sometime in Mid-November.