I don't have any easy answers to the "Micro first" vs "Macro first" debate when teaching Introduction to Economics. But this is what I do, and it seems to work a bit. And I have probably taught Intro about 30 times in my life. That experience should count for something.
1. We (Carleton University) are one of the last holdouts that refuses to split Intro Economics into two half courses. We are being "difficult". But I refuse to say someone has had an introduction to either micro or macro unless they have had an introduction to both. You need to be able to see it from both sides, or you can't really see it at all.
2. We start out with micro, BUT……………………..
I start out with a Production Possibilities Frontier. Apples and Bananas.
You can teach a helluva lot with just a PPF. And not just opportunity costs. What is the relation between the slope of the PPF and the relative price of apples and bananas? Why is the PPF curved, and what does it mean? (And unless you can answer that question, you do not understand why supply curves slope up.) And what does it mean if the economy is inside the PPF?
Next I teach comparative advantage and trade. For that you need two PPFs, with different slopes. You can call them "Farmer" and "Rancher", or you can call them "Canada" and "US".
I first assume barter. The Canadian BIB students know they can make a profit by "buying low and selling high". So they fill their canoe with Canadian apples, cross Lake Ontario, swap their apples for US bananas at the US relative price, then paddle home, swap their bananas for apples at the Canadian relative price, and find out they have more apples than when they started (minus what they ate while paddling). Which is their Profit! So other traders follow them, so Canadian and US relative prices converge. Standard stuff.
Then I introduce Money, and The Nightmare Scenario. Cue scary music. What happens if the dollar price of both apples and bananas is lower in the US than in Canada? Will free trade with those dastardly clever cheap productive Americans cause mass unemployment in Canada???
Then I talk about exchange rates. Whose "dollar" are we talking about? Yes, if the exchange rate is too high, The Nightmare Scenario would indeed happen.
But we don't blame free trade for The Nightmare Scenario; we blame the Bank of Canada, for keeping the exchange rate too high. The Bank of Canada should print money, to make the exchange rate drop, until Canada can export apples.
The alternative, under fixed exchange rates, is to wait for mass unemployment to cause Canadian wages and prices to drop, until Canada can export apples. Which might take some time.
Then I go on to all the regular micro stuff, like demand and supply curves. (Because demand and supply don't make any sense unless you understand why people trade. Which is why Mankiw does trade theory before demand and supply.)
I'm not saying it works perfectly, but it seems to work. The students understand that if the Bank of Canada gets it wrong, the economy will be inside the PPF, and all that opportunity cost stuff might not work. And it only takes about 20 minutes extra to teach it, on top of the regular micro stuff. It's totally unrigourous of course, but so what.
It probably works better in a smallish open economy like Canada; I'm not sure how I would do it if I were teaching in the US.
Worthwhile Canadian Initiative 
Oliver: totally wrong. Horribly wrong.
Your second sentence should be reversed: It is the curvature of the PPF that determines the slope of the supply curves of apples (and bananas), not vice versa. You can derive the PPF from technology and resources alone. Supply curves (if they exist) come later, when we add profit-maximising producers to the model.
“So, taking apples and bananas, if both are equal, the PPF will be concave and the efficient output will be 1/2 each.”
God no.
If A=B, that defines a 45 degree line ray from the origin, which picks a point on the PPF. It tells us nothing about the slope of the PPF at that point, and even less about how that slope changes as we move along the PPF (so A =/= B).
And there is nothing “efficient” about producing where A=B. Suppose nobody likes eating bananas?
Let me make it really easy for you:
Country 1 is an island, with 100 acres of identical land. Each acre can produce either a apples or b bananas. No labour needed. What is the slope and shape of the PPF?
Country 2 is a different island, that is very long and thin on a North/South axis, so land is not identical. And (a/b) steadily increases from South to North. What is the shape of the PPF?
@ Nick
🙂 Fair enough. I’ll give it more thought.
@ Avon
Criminals are RATIONAL? You sound like an architect lecturing the hoi polloi about how modern architecture is right. I know what you mean, the apparent contradictions can be addressed within the framework, but you still have a whole body of philosophy and social science telling you that it’s only one way to look at things and that it has well known short comings. There are reasons for the existence of the other social sciences and philosophy. In reading your comments, one wouldn’t know. And all rsj was saying to my mind, is that first year students should know.
Oliver: stop arguing with Avon, until you have answered my very simple 11.14 questions.
ok, sorry only just saw your last question. the ppf is more convex on the long island because the more apples are substituted for banans, the more banans will have to be grown on land actually more suitable for growing apples.
Oliver: correct as far as it goes, but not very precise. What is the shape and slope of the PPF on the first island?
“Country 1 is an island, with 100 acres of identical land. Each acre can produce either a apples or b bananas. No labour needed. What is the slope and shape of the PPF?”
Are you saying that if N = acres of land used for apples
0 <= N <= 100
A = Na
B = (100-N)b
?
Then the slope of the PPF is -b/a (if A is on the x-axis and B is on the y-axis). On those same axes, the PFF is a straight line: B = (100 – A/a)*b
How’d I do?
Tom: full marks on that (easy) question.
I prefer to write it as: 100 = A/a + B/b, but same thing.
Now, assume each acre is owned by one profit-maximising farmer (100 farmers in all). Let P be the price of apples in terms of bananas (so P=2 means 2 bananas trade for 1 apple). With P on the vertical axis, and A on the horizontal, what will the supply curve of apples look like?
The shape for the short island is a straight 45° line.
OK, thanks… but before I get to that, for Country 2 it appears that
dB/dA ~ A^(-1/2)
The PPF is a concave curve: B ~ b(100 – sqrt(2A/a_max))
You can replace “~” with “=” when a=0 in the extreme South, and a=a_max in the extreme north, linearly varying inbetween and b constant
Oliver: nope.
Tom: for country 2 (the long thin North-South island) you can’t give me a mathematical answer, because I only told you that a/b is an increasing function of latitude. I didn’t tell you what that function was. But you are right that the PPF is bowed out. Because the slope (with B on the vertical axis) is -b/a, which gets flatter (in absolute value) as you grow more and more bananas, pushing the margin of cultivation between apples and bananas further and further North.
Nick, you’re right: I can’t give you a formula. I made assumptions consistent w/ the problem, and did that problem instead. I also assumed a single contiguous apple growing area in the North, with the remainder to the South used for bananas.
Nick, what’s your favorite 1st year syllabus look like? (books and/or papers?)
Nick, would these be at all appropriate as part of a syllabus (say for any of the 1st four years)?:
Gary Becker’s 1962 paper “Irrational Behavior and Economic Theory” and Irving Fisher’s 1892 thesis “Mathematical Investigations in the Theory of Value and Prices?”
Tom: “I also assumed a single contiguous apple growing area in the North, with the remainder to the South used for bananas.”
That is not an assumption; it is a conclusion. It follows from the premise that a/b is an increasing function of latitude. If you grow some apples south of some bananas, you are inside the PPF, not on it. You could grow more of both fruits by rearranging what grows where.
No. Just read a first year text. Mankiw, Krugman, whatever.
“That is not an assumption; it is a conclusion.”… Good point! I knew there must have been a good reason I concluded that. ;^)
Tom: you are getting it.
Now solve for the apple (or banana) supply curve for country 1. (It might help you think about it more clearly if you put P on the horizontal axis and A on the vertical, because economists draw it the wrong way round, for obscure historical reasons). We want A as a function of P.
Hint: for each value of P, figure out what fruit would be most profitable for a farmer to grow.
Nick,
To start we should not write thing like 100 = A/a + B/b. Your apples and bananas form a tuple, you can’t add them.
Here’s the answer. Find the marginal rates associated with each input. The negative of the ratios give the marginal rate of technical substitution and RTS_A = RTS_B. (You can derive that condition from the full Lagrange multiplier set up or argue from market clearing). To simplify the notation here’s the problem:
u= x^ay^(1-a); v = (A-x)^b(B-y)^(1-b)
u are the apples, v are the bananas, A is the total amount of the first input and B is the total of the second. RTS_u = RTS_v:
u_x/u_y = v_x/v_y
where the subscript denotes partial differentiation. A bit of high school algebra yields:
y = Bb(1-a) x/[Aa(1-b) – (a-b) x]
which gives the PPF:
(u,v) = ( [Bb(1-a)/(Aa(1-b) – (a-b)x)]^(1-a) x, (A-x)^b[B(1- b(1-a)x/(Aa(1-b) -(a-b)x))]^(1-b) )
Now that you have u and v as functions of x, simple application of the chain rule gives du/dv. I’ll leave that one for you!
To answer your second question – I have never studied economics at school. But I have carefully worked through Mas-Colell Whinston and Green’s Micro Theory, Ljungqvist and Sargent’s Recursive Macro, Hamilton’s Time Series Analysis, Greene’s Econometric Analysis Cochrane’s Asset Pricing, Romer’s Advanced Macro, and Osborne and Rubinstein’s Game Theory text. And that’s just the my core econ – I’ve read far more math finance, which is my actual speciality. I have so much fun with this stuff, I take it on vacation with me, seriously. My wife has to pry it out of my hands.
I see Tom has answered correctly. I’m afraid I can’t do the math. But to see whether I at least understood correctly in hindsight: The slope is determined by the relative price of one good in terms of the other. It is straight on the short island because marginal cost of each good in terms of the other remains equal, irrespective of the mix of goods? But it cannot be said to be 45° because you didn’t specify how apples exchange for bananas and thus can only be presented as a relation?
In any case, thanks for the free lesson. I doubt I’ll ever reach any level of proficiency in anything involving even the slightest bit of math. At the very least I’ll have to save that task for when the kids grow older and I get to sleep & read again. And god knows what I learnt back in business school. I only vaguely remember the macro intro class (Volkswirtschaft) and slighty more clearly law and accounting. But none of the above rung the faintest bell. So in case it wasn’t apparent, I just threw everything together ad hoc by skimming through the internet while pretending to work. I hope that my public display of ignorance is repentance enough for what I regret came across as arrogance. That was not intended.
But I still remain curious whether you, Nick or Frances, consider Avon’s statement ‘criminals are rational’ to be A)universally true or, if not, at least B) indispensable for practicing economics? Which I realise is quite separate from asking whether such an assumption can be useful or not – something I am certainly not qualified to opine about.
Full marks to Avon (I think).
But what I wanted to prove is that if a=b the PPF is a straight line, and if a=/=b the PPF is bowed out. I should be able to prove that by differentiating the PPF twice. (Note the “should”.) I was hoping this would be simpler, so I could do a very simple intuitive post on this.
And that is important because a=b is very unlikely to be true, and if a =/= b, so the PPF is bowed out, the supply curve for apples (and bananas) will slope up. Which is something I wanted to explain to rsj.
“To start we should not write thing like 100 = A/a + B/b. Your apples and bananas form a tuple, you can’t add them.”
I don’t understand you there. A/a is amount of land needed to grow apples, and B/b is amount of land needed to grow bananas. We can add them. It’s just the resource constraint.
Well done on the reading. And I know that intro texts are written in babytalk. But I still think you would gain by holding your nose and reading/skimming one. There’s a breadth/depth trade off. I would be very surprised if you found nothing interesting.
Oliver: I give you credit for trying. Let me make some small changes to correct what you said:
” But to see whether I at least understood correctly in hindsight: The slope [of the PPF] is determined by the [marginal opportunity cost] of one good in terms of the other. It is straight on the short island because marginal [opportunity] cost of each good in terms of the other remains [constant], irrespective of the mix of goods? But it cannot be said to be 45° because [it would only be -45 if a=b]”
Yep.
The slope is -a/b (or -b/a, depending what’s on which axis). Which is a constant in country 1.
And profit maximising farmers will choose to grow apples or bananas according to whether Pa/Pb (the relative market price of apples in terms of bananas is > or < (b/a). So the supply curve of apples will be perfectly elastic (horizontal, with Pa/Pb on the vertical axis and A on the horizontal) at a height of b/a. Ditto for the supply curve of bananas, except its at a/b. And this means that in competitive equilibrium (as long as people consume some of both goods) Pa/Pb = b/a.
For country 2, the slope of the PPF is still -a/b, but a/b is not a constant. As you grow more and more bananas, pushing the margin of cultivation north, a/b gets bigger, so the marginal opportunity cost of a banana increases. (Ditto for apples.) Which is why the PPF is bowed out, and why supply curves slope up, except in the very special case where all land is identical.
“Criminals are rational” is useful. We can always posit a utility function that makes it universally true, but then it may no longer be useful. Why did he do X? Because he likes doing X. Where X is anything whatsoever. Why did he do X yesterday, but Y today? Because he liked doing X yesterday, and likes doing Y today. We need some sort of stability of preferences across people and across time, if it’s going to be useful. And that’s even before we start talking about beliefs.
Rationality is not strictly essential for practicing economics. But economics would be very different without it, and we would need to replace it with something else.
Nick,
For an intro text, I read Hal Varian’s Intermediate Micro. That’s a nice book, I like it very much, but it shows the difference between the expectations of physics students and economics students at the undergrad level. Baby Varian is often used as a second year text but most of Mas-Colell Whinston and Green is at the level of upper second year physics. What I would like to see is baby Varian used in first year (but calculus based) and Mas-Colell Whinston and Green started in second year. That is how a physics curriculum would treat micro theory. In fairness, the top of the econ field catches up completely by the end of grad school and the top of econ is as every bit as technical as physics. I have deep respect for it. The problem is that so many people want to take econ at the undergrad level (the joys of subsidized post secondary education), there is no way the discipline can be treated seriously until grad school. The graduating class in a typical physics department from 4th year is less than 10 at Carleton (maybe less than 5). Most go to grad school. I bet econ majors out numbered the physicists by 20 to 1 at least, and almost none go to grad school. They wouldn’t have even gotten through second year if held to the same standard as physics. Take a walk over to the physics department, Nick, you’ll see what I’m talking about.
You need to be careful what adding variables with different units. What’s 3 kilogram + 2 metres? Apples and bananas carry different units. When you see budget constraints on a graph with quantities, they have implicitly converted units, usually to prices or made the system unitless by some other conversion. Treat the problem as a tuple and then solve.
I’ve been trying to keep away from this comment section because I have a lot of work to do but I just can’t resist.
@Oliver
A big part of the problem is that being ‘rational’ means something very different in economics jargon. Perhaps you know that already but if so it doesn’t seem like the point has sunk in.
Take an example: A man goes to a club with some acquaintances. These are not close friends of his so he may never meet them again and they have no influence over his career. He drinks “far too much” which makes him throw up on the way home. The next day he is stuck with a pounding headache which makes it hard for him to focus at work and he makes several mistakes. Was this person being rational when he drank too much?
Regular person: No of course not! Drinking gave him only a little pleasure while throwing up and the headache harmed him greatly. His overall well-being was clearly reduced as a result and therefore it was not rational of him to drink as much as he did.
Economist: Yes. His actions that evening show that he did not at the time care much about how he would feel the next day or even later that evening (he heavily discounted the future). The man may also have believed that the cost (having to think about something he doesn’t want to) of considering the consequences of his actions was larger than the benefit. It would then be a case of imperfect information. In sum: given his constraints and the information he had available the man was rational in his drinking behaviour.
With this kind of reasoning criminals are always “rational”. I honestly think it would be better if we made up some jargon word and used that instead since there are times when even economists mix up economics rationality with common sense rationality (and plenty of times when they give the wrong impression to journalists and the general public because they use this word).
Nick,
Are you doing macro or micro? Because I thought this was micro. It costs $100 million to develop a drug and then 1 penny to make each pill. The drug company is willing to sell 1 pill for $100 million + 1 penny. 2 pills for $50 million plus 2 pennies. Etc. As the quantity increases, the price per pill that the company is willing to supply those pills at decreases. What is the shape of the supply curve?
If many people travel between two points, an airline can use a bigger plane, which means that it is cheaper, per passenger, to transport those passengers. What would the supply curve be for the airline?
A word processing program costs $100 million to make. What is the shape of the supply curve for the company that sells this program?
Reading over Adam Smith’s remarks about division of labor, what do you think the supply curve is of his Pin factory?
The fact that this doesn’t aggregate nicely into a “you have one island that you spend half the territory growing apples and half bananas” is not my problem. It just doesn’t aggregate nicely and firms need to find some way to survive, or in the case of airlines, of going bankrupt gracefully.
But given that this is the most common state of affairs, shouldn’t we be teaching it?
rsj: “Are you doing macro or micro?”
Good question. In this case I am doing General Equilibrium theory, which is usually said to be part of micro, but is about the economy as a whole. Yep, micro supply curves are a GE phenomenon.
BTW, let’s switch this PPF/supply curve stuff to my new post. See the end bit of my new post, on Increasing Returns to Scale. (Though I’m not happy with that bit yet.)
” I honestly think it would be better if we made up some jargon word and used that instead since there are times when even economists mix up economics rationality with common sense rationality”
Consistency (since there is that implicit assumption that preferences don’t change from one situation to the next buried in there). Or (I think it was David Colander who suggested it) “purposefulness”
For the record: I should have written “convex” and my math as a bit off, even for the problem I did solve. For that problem:
B = b10sqrt(100 – 2A/a_max), and dB/dA = (-b/a_max)/sqrt(1 – 2A/(a_max*100)). I think. I’m sure nobody cares.
I care Tom.
rsj,
Everything you’ve talked about is covered in a basic introduction to micro. Seriously, read something like Hal Varian’s Intermediate Micro. Work out the details for yourself. Your basic misunderstandings is like saying physics has all wrong – heavy things fall faster than light things in gravity fields. It’s clear, just look at it – a feather falls slower than a bowling ball so all this physics nonsense that say everything falls with the same acceleration is just silly! Seriously, you look that foolish.
Nick,
Good question. In this case I am doing General Equilibrium theory, which is usually said to be part of micro, but is about the economy as a whole. Yep, micro supply curves are a GE phenomenon.
OK, but you are not going to get a Law of Supply from GE. You wont even get a law of Demand. GE gives you very little beyond existence. The fact that (I hope) we all agree that, at a minimum, MC firms are the norm + IRS and large fixed costs are also the norm means that supply curves, as commonly introduced to first year students, should be shown to go down rather than up. You can say, “Well these firms — i.e. pretty much all firms — don’t actually have supply curves”, in which case why teach the scissors as the basis of what a first year will remember? They are not going to remember the SMD, they will remember the scissors, and they will vote accordingly, creating a lot of misinformed, yet smug voters who think they know what’s going on because they read a first year text.
I’ll take a look at your next post, at which point I will needle you about revolving capital.
“By the way, and this question is for all of you commenting here: have you ever taken Intro Economics, or read an Intro economics textbook?”
Nick, do you think I took an Intro Economics course?
What grades do you think I get/got in school?
“And a second question, for rsj: Assume increasing returns to scale. For example assume Q = L – F where L is labour input and F is some fixed cost. Assume the firm maximises profit. What is the slope of the supply curve? (Yes, it’s a trick question, and the real question is to tell me why it’s a trick question).”
I am going to try this one. I am probably missing the point on this one. I might be making a different point. With fixed costs, is it possible that the supply curve slopes both up and down?
hello Nick, I have a question (off-topic)
I’ve read you before referring to Canada as a ‘small’ open economy and I was wondering what is the metric you use?
I (think I) know from my international macro that to be ‘big’ in that context, you need to be able to influence the international interest rate or, what seems to be equivalent, to be able to exert an influence on global savings/investment decisions
Is Canada ‘small’ in that sense?
thank you
john: well, we normally reckon that Canada is about one tenth the size of the US, which is about one quarter the world economy. So if canadian saving or investment increased by 100% (which is very big), that would increase world saving or investment by around 2.5%. Yep, small enough to ignore, given all the other things we ignore when we build a model.