UPDATE: Here is the 12/25/2016 version of the book.
To be clear, the typical econ 101 book or intermediate micro book tells you the objective of the consumer. You are told the aggregate demand curve or the utility function and then you grind out a solution. I do the opposite in my book. I tell you the choice the economic agent made and then I ask you; "what must be the agent's preferences or expectations that could explain this choice?" This inverse problem is what economists really do for a living while in our textbooks we don't bother to teach this. If you read the full problem below, you will see that I have the ambition to teach students "set identification" as freshmen. Let's push our students to think! Let's make economics great again!
Let me share one set of problems with you. If this interests you, then you will want to read this $1 book.
New Problem
Many people own long lived durables such as cars or homes. These products use energy. This has two implications. First, the people who purchase these products face a tradeoff between paying more upfront versus bearing higher operating expenses (i.e paying for energy and gasoline to operate these products). Second, both the consumption of gasoline and electricity has environmental consequences. More fuel efficient vehicles such as the Toyota Prius use less gasoline per mile of driving.
Consider the demand for a new car. The owner will drive this car for three years and then sell it for $500. To keep this problem simple, we will assume the market interest rate is 0% each year. Suppose that Matthew drives 10,000 miles each year. He is choosing between a Prius and a Honda Civic. He views these cars as perfect substitutes (meaning they have the same attributes) but the Prius achieves 50 miles per gallon while the Honda Civic achieves 35 miles per gallon.
Here are the data on Matt’s annual operating expenditure for each car
Car
|
Price of Gasoline
In 2017 is $3
|
Expected Price of gasoline in 2018 is $3
|
Expected Price of gasoline in 2019 is
$4
|
Prius
|
(10000/50)*3
|
(10000/50)*3
|
(10000/50)*4
|
Civic
|
(10000/35)*3
|
(10000/35)*3
|
(10000/35)*4
|
If the Prius is priced at $26500 and the Civic is priced at $23,000 , which car will he buy?
Answer
The upfront price difference for the two cars is $3,500 such that the Prius is $3,500 more expensive but its operating costs are lower. How much lower? The full cost of operating the Prius equals 200*3 + 200*3 + 800 = $2,000. The full cost of operating the Civic = $2,857 so the Civic is the cheaper car to purchase and operate.
New Problem
Let us repeat this exact same problem but make one important change to the this problem. Note that in the previous problem we assumed that Matt knew the future price of gasoline. In the year 2017, he knew that the price of gasoline in 2018 would be $3 per gallon and that it would be $4 in 2019. In reality, we do not have perfect foresight about the future. So, in this problem we will be more realistic and introduce the variable “X” which represents Matt’s best guess of the price of gasoline in 2018 and 2019. To keep the algebra simple, let’s assume that whatever Matt thinks is the price of gas in 2018 is also his guess for 2019.
Here are the data on Matt’s annual operating expenditure for each car
Car
|
Price of Gasoline
In 2017 is $3
|
Expected Price of gasoline in 2018 is $X
|
Expected Price of gasoline in 2019 is
$X
|
Prius
|
(10000/50)*3
|
(10000/50)*X
|
(10000/50)*X
|
Civic
|
(10000/35)*3
|
(10000/35)*X
|
(10000/35)*X
|
If the Prius is priced at $26500 and the Civic is priced at $23,000 and we observe that Matt buys the Prius, what have we learned about X?
Answer
Matt is a cost minimizer. He will only buy the Prius if the cost of buying it and operating it is less than the cost of buying the Civic and operating it.
Cost of buying and operating the Prius = 26500 + 600 + 400*X
Cost of buying and operating the Civic = 23000 + 3*286 +286*X + 286*X
If Cost of buying and operating the Prius < Cost of buying and operating the Civic then;
27100 +400*X < 23858 + 572*X
27100-23858 < 172*X
Then X > $18.84
If the price of gasoline is expected to soar over $18.84 then it is rational to purchase the Prius.
New Problem
Same setup again but now let’s relax the assumption that Matt drives 10,000 miles. Instead only he knows how many miles he drives and to make this simple. Let’s assume that he drives M miles each year and regardless of what type of car he drives. In this case;
Car
|
Price of Gasoline
In 2017 is $3
|
Expected Price of gasoline in 2018 is $X
|
Expected Price of gasoline in 2019 is
$X
|
Prius
|
(M/50)*3
|
(M/50)*X
|
(M/50)*X
|
Civic
|
(M/35)*3
|
(M/35)*X
|
(M/35)*X
|
If the Prius is priced at $26500 and the Civic is priced at $23,000 and we observe that Matt buys the Prius, what have we learned about X and M?
To provide some intuition, if Matt drives 20,000 in 2017 then his operating expenses if he owns a Prius equals (set M=20,000) 400*3 = $1200.
Answer
Matt is a cost minimizer. He will only buy the Prius if the cost of buying it and operating it is less than the cost of buying the Civic and operating it.
Cost of buying and operating the Prius = 26500 + (M/50)*(3+2*X)
Cost of buying and operating the Civic = 23000 + (M/35)*(3+2*X)
If Cost of buying and operating the Prius < Cost of buying and operating the Civic then;
26500 + (M/50)*(3+2*X) < 23000 + (M/35)*(3+2*X)
3500 + (7*M/350)*(3+2*X) < (10*M/350)*(3+2*X)
3500 < (3*M/350)*(3+2*X)
So, any combination of M and X that satisfy this inequality will lead to Matt to buy the Prius. For example if M = 25,000 (so he is a heavy driver), we can solve for X
3500 < (75000/350)*(3+2*X)
3500 < 214*3 + 428*X
And X=$6.67. So a heavy driver for whom M=20,000 will buy the Prius in this economy if he expects X to be greater than or equal to 6.67.
A key point in this example is the observed discrete choice of investing in the fuel efficient Prius is that we “set identify” the combination of M and X (miles driven and expectations of future gas prices) such that it is rational to purchase the fuel efficient vehicle. In terms of our initial discussion of detective work from the clues we observe in this case we have not uniquely figured out “who did it” but we have a set of possible candidates (the M,X pairs).