Worthwhile Canadian Initiative

Inequality and competition in a digital economy: a case study

Pokémon Go is an economy in miniature. There is exchange: players trade Pokémons and swap gifts. There is scarcity: the balls required to catch Pokémons are scarce, as is Pokémon storage capacity and other items in the game. There is production: through various activities, such as walking a Pokémon egg, or leaving a Pokémon in a gym, players can produce new Pokémon, or earn tokens. There is status seeking and signaling: high rank players parade their skill by wearing special clothing, and displaying their game level. There are even exports and imports. Pokémon Go imports dollars from the real life economy, exporting in exchange game tokens, and the enjoyment and entertainment players get from using those tokens.

Yet Pokémon Go differs from the real-world economy in two crucial respects. First, prices, the distribution of initial endowments, and all rules are determined by the game manufacturer, Niantic, which acts as an omnipotent “social planner”.  Second, anyone who does not like the rules of the game is free to leave. The possibility of exit gives power to players: because more players=more revenue, the social planner has a strong incentive to set rules that keep players happy. Thus the rules that govern the Pokémon Go economy provide insight into what type of economic rules people would choose, if they actually had power to influence the social planner’s decisions in real life. 

One of the most notable features of the Pokémon Go economy is the number of rules that limit the extent of inequality. Players earn tokens by leaving their Pokémon in gyms – up to a maximum of 50 tokens a day. Players gain status by achieving higher levels – but the game is structured so that the overwhelming majority of players are somewhere between level 30 and level 40. Players gain the ability to defeat other players in battle by powering up stronger Pokémon – but each Pokémon’s maximum combat power is capped too.

But so what? Pokémon Go is just a game, after all.

Alpha Beta and the Libra Twist

Suppose I promise to be in the same place as you; but you make no promise to be in the same place as me. Then I am Beta follower and you are Alpha leader; because you go where you want to go and I must go to the same place to keep my promise.

We get the same Alpha-Beta relationship with asymmetrical fixed exchange rates. If the US Fed decided (for some unknown reason) to peg the exchange rate of the US dollar to the Canadian dollar, but the Bank of Canada makes no such promise the other way, then the US Fed becomes the Beta follower and the Bank of Canada becomes the Alpha leader. US monetary policy is now decided in Ottawa.

It's the same Alpha-Beta relationship between central bank and commercial banks. The Bank of Montreal pegs the exchange rate of the BMO dollar to the Bank of Canada dollar; but not vice versa. So the Bank of Montreal is Beta follower to the Bank of Canada's Alpha leader. The Bank of Canada decides Canadian monetary policy, not the Bank of Montreal.

Now let's add the Libra twist to this simple story.

Suppose I promise to be at a point midway between you and Alice; but you and Alice make no promises about where you will be relative to me. I am Beta follower. But Alpha leadership is now shared 50-50 between you and Alice.

If I understand it correctly (I quite possibly don't) Facebook's new Libra currency is supposed to be pegged to a basket of international currencies. Libra is then a Beta follower, just like a normal commercial bank. But unlike a normal commercial bank, which follows only one Alpha leader central bank, Libra will be following a basket of several central banks. So Alpha leadership is now shared (in proportion to those basket weights) between those central banks.

Which is an interesting twist.

My guess is that Libra will not take off into wide usage (JP Koning's good post explains why). But suppose it does take off, and replaces the money created by normal commercial banks which follow only one central bank each. What happens if the US Fed wants to loosen world monetary policy and the ECB wants to tighten? It's like you and Alice both running off in opposite directions, each trying to run faster than the other, to get me to follow in your direction rather than her direction and vice versa.

Update: it's like Libra creates the incentive for a Tug-of-War between the Fed and the ECB, with Libra tied to the middle of the rope. Except that it's not a rope but a very elastic rubber band.

This doesn't look like a stable equilibrium to me.

Reflections on Westeros

Well, it is the May long weekend and a celebration of Queen Victoria but this year it has also coincided with the end of Game of Thrones and its own set of Kings, Queens and associated dysfunctional noble figures.  There has been a lot of angst expressed about how inadequate the final season has been in terms of plot and character development and the reviews are mixed, but I will leave such matters to others. I want to focus on some other things of a more economic and political nature.

Aside from the visuals of what appears to be a Rostowian pre-takeoff economy marked by low levels of productivity, low technology and a land centered economy with a feudal type of organization, remarkably little insight was offered over the eight seasons as to what the mechanics of the economy were that marked the Seven Kingdoms of Westeros.  Indeed, given the amount of war and pillaging that inevitably must have disrupted trade routes and commerce, it is a surprise that anything was produced at all aside from a thriving weapons and armour industry.  Even the effects of climate change as the endless winter approached did not appear to spark much in the way of policy debate.  And there does appear to have been an abundance of government deficit financing with a monetary institution known as the Iron Bank holding many of the loans.  In the end, the Seven Kingdoms appear locked into a pre-industrial stasis and need some type of political and economic reforms as well as an enclosure movement and a learning focused Renaissance to boost agricultural productivity and ignite an industrial revolution.  However, the last episode suggests that the governing elites are not about to set out on the path of any social, economic or institutional innovations given the shocks of external invasion by zombie like White Walkers and the ultimate battle for the kingdom.

Bicycle Disequilibrium Theory

Suppose you need a bicycle to get to work. Suppose bicycles are a common property resource, because bike locks don't work. Every night the workers deposit their bicycles in the bike bank, and in the morning it's first come first served. And suppose that sometimes there aren't enough bicycles to go around. So sometimes the level of employment is determined by the number of bicycles, and not by all the usual stuff.

Any individual can always get a bicycle in the morning, simply by getting up early enough. But in aggregate they can't. Fallacy of composition. A theory of when workers wake up might be interesting, and useful for microeconomists wanting to understand the distribution of employment, but it won't help us understand what determines the aggregate level of employment.

Bicycle disequilibrium theory helps us understand what determines the level of employment and output. It also helps us understand other puzzling phenomena, like why workers sometimes wake up and go to work so ridiculously early.

Is the Russia-America Global CoDominium About to Begin?

In the wake of the Putin-Trump Helsinki summit, there is much speculation about what was actually said between Putin and Trump behind closed doors and the uncertainty spread throughout the American government about whether agreements had been reached on issues such as Syria and the Ukraine.  The subsequent invitation to Putin to visit the White house in the fall – probably just before the November elections – has resulted in further uncertainty especially after Putin’s statement that he proposed to Trump holding a referendum to resolve the eastern Ukraine issue.  So, what is really going on here?

Quite frankly, we have all been scratching our heads as the behaviour in some respects is reminiscent of 18^th and 19^th century monarchs gathering to decide the fate of wide swaths of the world in private meetings.  Putin is an autocrat and Trump is a business autocrat who admires political autocrats, so their personal level diplomacy may indeed be a series of moves designed to remake the world and return it to an age when Russian and American led blocs were the only game in town. Both the Russians and the Americans have seen their political influence decline in a multilateral world led by growing Asia-Pacific economies and both countries have been less than comfortable with the rise of China.

The Tale of the Two Cobblers (collusive price cuts)

Mostly for fun, and teaching. But I think it might matter.

A village had two cobblers. The right-handed cobbler was best at making right shoes. The left-handed cobbler was best at making left shoes. So the villagers would buy one shoe from each cobbler.

Other villages were some distance away, so the cobblers had monopoly power and faced downward-sloping demand curves for their shoes. Each cobbler set a price to maximise individual profits, taking the other cobbler's price as given. The cobblers were in a Bertrand equilibrium, except the two goods are strict complements, rather than substitutes as is normally assumed.

Then one day the two cobblers fell in love, got married, and set the price for a pair of shoes to maximise their joint profits. They set a price that was lower than the price of a pair of shoes when they were single. The cobblers were happy because their profits were higher. And the other villagers were happy too, because the price of shoes was lower.

Is this (one reason) why firms exist?

Math appendix:

Marginal Revenue is (1-(1/E))P where E is Elasticity of demand and P is Price. A profit-maximising firm wants Quantity sold where Marginal Revenue equals Marginal Cost, and so sets price at P = [1/(1-(1/E))]MC.

The demand function for shoes is Q_R = Q_L = D(P_R+P_L), where (P_R+P_L) is the price of a pair of shoes. If P_R=P_L initially, a 1% cut in P_R, holding P_L constant, will cause only a 0.5% cut in (P_R+P_L), so the elasticity of demand for right shoes (or left shoes) is half the elasticity of demand for pairs of shoes. So when the two cobblers merge, elasticity doubles, and they set Price as a smaller markup over Marginal Cost.

In the initial Bertrand equilibrium, a small cut in P_R, holding P_L constant, will have a negligible effect on profits from right shoes (since we are starting at a point where P_R maximises profits from right shoes). But it will increase the demand for left shoes, and so increase profits from left shoes. So if the two cobblers collude, they would want to collude to cut prices. And each individual cobbler has an incentive to cheat on the collusive agreement by raising price above the joint-profit-maximising price. It's the opposite of the standard case where the two goods are substitutes.

We could relax the assumption of strict complementarity. Results would be similar in any example where the two goods are complements rather than substitutes. Because if one firm cuts price it increases (rather than reduces) the other firm's demand and profits. Mergers and collusion will result in lower rather than higher markups of price over marginal cost.

[I vaguely remember reading about a river in Germany(?) where all the jurisdictions along the river collected a toll on passing boats. And how the sum of the individual revenue-maximising tolls was bigger than the joint revenue-maximising toll. But that's all I can remember. Update: Alex Tabarrok on Twitter tells me it's the "Rhine River Problem", originally from Cournot. In Cournot equilibrium firms set quantities taking other firms' quantities as given (in Bertrand equilibrium firms set prices taking other firms' prices as given). The Cournot equilibrium for the two cobblers is a corner solution where both sell zero shoes (because selling slightly fewer right than left shoes means left shoes have a zero price so the right cobbler gets all the revenue).]

"Profits = Investment - Saving"

Or, "Profits = Expenditure - Income". Those are just alternative ways of saying the same thing, for a closed economy, if investment and saving include government investment and saving.

Most economists will say that's wrong. And it is wrong by standard definitions, where aggregate expenditure and income are the same thing, and investment and saving are also the same thing (for a closed economy, including government investment and saving).

But let me tell you a story:

There are firms and households (ignore government and foreigners). Firms rent land and labour from households, and use it to produce food which they sell to households (ignore capital). There is a fixed stock of currency that is used to buy and sell everything. Food cannot be stored. No other assets.

In any given year, if households spend $100 more buying food than the income they earn from rent and wages, then at the end of the year households own $100 less currency and firms own $100 more currency than at the beginning of the year. Firms have made a profit exactly equal to the $100 difference between households' expenditure and income. Or, firms' $100 profits are equal to households' negative saving (there is no capital and no investment in this story).

But who owns the firms?

If households own the firms, we can say that firms' assets are owned by households, and firms' profits are included in households' income. And if we do that, then we are back at the standard definitions where Expenditure = Income, and Investment = Saving, must always be true.

Or we could adopt an intermediate position: we could say that firms' profits are part of household income only if firms actually distribute those profits to the households that own them. In which case we get: Undistributed Profits = Expenditure - Income = investment - Saving.

There's a number of different ways we could add things up. Which is the best way? It depends.

Suppose firms were like a strange religious cult; they save all their profits for six years, then on the seventh year they blow the lot by spending it all on food which they burn as a sacrifice to the gods. None of the households want firms to do that; it's just what firms do, following some weird internal logic of their organisational structure. If so, you had better build that fact about firms' behaviour into your macroeconomic model. And it would not make sense to include firms' profits as part of households' income, because households know they will never be able to consume firms' profits. (And a corporate profit tax might really be a tax on corporations, and not on the households who own them, work for them, or buy from them.) So Profits = Expenditure - Income = Investment - Saving.

There is no one right way to do the accounting (though there are conventional ways, and it's easier to understand what others are saying if we all follow the same conventions). The accounting can't tell you what the world looks like (though it can help you keep your head straight when you are looking at the world). First decide what the world looks like; then do your accounting accordingly.

[An economist will probably make a comment on this post, and that comment will go automatically into the spam folder. Because Typepad, and history, across this and other macro blogs. But if it's a reasonable comment I will fish it out, after a short delay.]

A Balassa Samuelson theory of negative real interest rates despite productive investment and impatient representative agent

I think this is right (but I can't do the math to work out an example to be sure, though any competent grad student could). The idea is that you can get negative interest rates, despite productive investment and impatient consumers, because the prices of the goods you can invest to produce more of will be falling over time relative to goods you can't invest to produce more of. It might be a theoretical curiosum, but it might also be empirically relevant, with falling prices of manufactured goods and falling share of expenditure on manufactured goods, relative to services. And all that.

[And of course, I figure out this model of negative real rates just as it looks like the Bank of Canada will be raising rates soon. Oh well. They are still not very high.]

Here's a toy model, just to illustrate the basic idea:

How can Halloween get started?

A day late, but whatever.

It's easy to understand how money might get started. A non-smoker accepts cigarettes(pdf) he doesn't want in exchange for the jam he doesn't want. Then finds a smoker who will accept those cigarettes in exchange for biscuits he does want. That non-smoker has just used cigarettes as a medium of exchange -- as money -- to get around the problem of a double-coincidence of wants. And once the ball starts rolling, it can snowball, because there's now one extra person who accepts cigarettes in exchange for other goods, which makes other non-smokers more willing to accept them, because they can exchange them with the first person, which makes cigarettes a more liquid asset, and so better as money. And so on.

The Devil You Know vs The Market For Lemons

I told my friend Mike I was thinking of trading my car in for one that used less gas. Nowadays I would talk about the Market for Lemons as a reason against doing what I was thinking of doing. But in 1974 I didn't know about Akerlof's famous paper, and neither did Mike, who was majoring in music. "Better to stick with the devil you know" he said.

"The Devil you know" and "the Market for Lemons" are similar: both use asymmetric information (the seller knows more about the car than the prospective buyer) to explain a low volume of trade. But they are not the same. A thought-experiment can explain the difference.

Suppose the government made a surprise announcement: everybody who owns a used car must sell it next week to the highest bidder. If you still want a car you must sell yours and buy someone else's.

Making sales compulsory solves the Market for Lemons problem. The sample of cars offered for sale represents the whole population of cars; those who know their own car is a cream puff can't hold it back from the market. If the Market for Lemons was the only problem in the used car market, then the compulsory universal sale would improve efficiency in the allocation of cars. People who found themselves needing to drive more miles could sell their gas guzzlers to the people who found themselves driving fewer miles.

But universal compulsory sales of cars does not solve the Devil You Know problem.

First there's simple risk aversion. Suppose everyone knows that half the cars need a $1,000 repair and the other half don't, but only the seller knows if his own car needs that repair. Sellers of lemons have a 50% chance of winning $1,000, which is worth less than a certain $500 if they are risk-averse. Sellers of cream puffs know they have a 50% chance of losing $1,000, which is worth more than a certain $500 loss if they are risk-averse. (Remember that everyone buys a car for the same price they sell their car, so price is a wash, if this is the only difference.) The value of the expected gains to the expected gainers are worth less than the value of the expected losses to the expected losers.

Second, even if everyone is risk-neutral, there's the problem of not knowing what particular repairs are needed. If your car needs to have the brake pads replaced soon, it's better to know that fact before they wear down too much and you need to replace the rotors too (or worse). And if your car won't start on a cold morning, or overheats on hot days, it's better to know that fact in advance, so you can plan accordingly.

[And if the government's surprise announcement is not a surprise, but is announced well in advance, there's an additional problem. Nobody will change the oil if they know they are going to sell the car anyway. But that's the standard Moral Hazard problem, which is distinct from the Devil You Know problem.]

I wonder which problem matters more, in the used car market. Or in finance?

I started to think about the Devil You Know when thinking about the choice of textbook for Intro Economics. You never really know the flaws in a textbook until you have taught from it. Changing textbooks is always risky; and the flaws catch the teacher unprepared. Most of our switches have gone OK, but one didn't.

Monetary Policy for a central bank with no balance sheet

How a central bank can do things with words.

Imagine a central bank with no assets and no liabilities. It does not issue money. It does not buy or sell anything. It does not regulate the commercial banks. The only thing it controls is one word in the dictionary. Every morning it edits the dictionary, announcing what the word "dollar" means today.

If nobody uses the word "dollar", then the central bank is irrelevant. But if people do use the word "dollar", the central bank's monetary policy can have real effects.

To make my thought-experiment semi-concrete, imagine that people use Bitcoin as medium of exchange. All goods and services, and financial assets, are bought and sold for Bitcoin. But to keep it simple, I will ignore Bitcoin mining; there is a fixed stock of Bitcoin. But "dollar" remains the unit of account, from force of custom, even though dollars no longer exist.

Suppose one morning the central bank announces that "one dollar" now means "0.5 Bitcoin", and not "1.0 Bitcoin" like it meant yesterday.

Financial Assets > Liabilities

Take Bitcoin for example. It's a financial asset to whoever holds it. To whom is it a financial liability? I suppose you could say "it is a liability to the whole community of those who accept Bitcoin in exchange for goods". But that answer seems like a desperate attempt to salvage the assets=liabilities dogma. Nobody is obligated to accept Bitcoin.

Here's the right way to think about it. It's quite simple really. Very basic economics.

Suppose I sell you my car for $2,000. That would only happen if I value my car at less than $2,000, and you value my car at more than $2,000. So when I sell you my car, it must mean that the value of the car increases.

Monetary Science Fiction

Chris Dillow says that economics is like literature. Maybe it is, and maybe it isn't. But if it is literature, economics needs more science fiction. Paradoxically, imagining radically different worlds can help us understand better how the actual world works, as well as helping us consider policy alternatives.

Imagine a world where all borrowing and lending is banned. You cannot lend anyone money, whether you lend it at a fixed interest rate, or at 0% interest, or in return for a share of the profits. Neither individuals nor corporations (including governments) can borrow or lend.

How would monetary policy work in that world?

Do (local) housing demand curves slope up?

Take this post with a truckload of salt. This is a second in my series in which "Lost Macro Farmboy tries to get his head around Urban Economics". Think of it as sceptical pushback. I might easily be wrong, but those who know a lot more Urban Economics than I do should be able to explain why I'm wrong.

If the demand curve for X slopes up, a rightward shift in the supply curve of X (caused by relaxing legal restrictions on producing X) will cause a rise in the price of X.

Why might the demand curve for X slope up? One reason might be strong strategic complementarities, like network effects. The more people who own a phone, the bigger will be the benefit to me of having a phone, and the greater the price I would be just willing to pay to buy a phone.

Question: Why do cities exist? Why isn't population density the same everywhere inside any country?

I can think of two plausible answers:

1. Natural geography matters. Countries are not flat featureless plains. Some places are more desirable than others to live and work. For example, you will tend to see cities located at natural harbours.
2. Strong Strategic Complementarity. Let me explain what I mean by that.

Some Simple Basic Money, for Finance People

Finance people are good people. Economics needs finance people. Some of my best friends are finance people. But (you heard that "but" coming), finance people (though there are of course honourable exceptions) just don't seem to get money.

I can hear the reply now: "Yeah, and money people don't get finance either!". And I think you are right, but only half right, about that. I think that money people do get simple basic finance; it's the more complicated stuff we don't get. But finance people, it seems to me, often don't get the simple basic stuff about money.

And that's not because money people are smarter than finance people (though we are better-looking). It's because money is weird. Money is not like other assets. So when you take simple basic finance theory, that works OK for other assets, and apply it to money, you can get in a mess.

I watched a finance person on Twitter ask the question: what determines the market value of a zero-coupon perpetuity, like currency? That's a very good question to ask, but you won't get a sensible answer if you do a standard Present Value calculation of a perpetual stream of zeros. Why isn't it zero??

New Keynesian macro when all output is consumer durables [DRAFT]

Warning: math-challenged economist at play. I want to see if I can sucker any readers into checking my math and doing the rest of the math for me. Do not read this post unless you think that might be fun.

Update: Keshav has solved the math. Now we are trying to understand what it means.

The simplest New Keynesian macro model assumes all output is consumer goods. The structure is U(t)=U(C(t)) and C(t)=Y(t), where C(t) is consumption and Y(t) is output at time t.

I want to assume instead that all output is consumer durables. The new structure is U(t)=U(C(t)) and C(t)=K(t)=(1-d)K(t-1)+Y(t). Where K(t) is the stock of consumer durables owned by the representative agent and d is the depreciation rate. Each unit of consumer durables provides one unit of consumption services per period.

I think New Keynesian macroeconomists will see this as a friendly amendment. Because theirs is a special case (where d=1) of my more general case. It is true that some consumption goods are more durable than others, but assuming the average consumer good has at least some durability is more plausible than assuming it has none. And since it is purchases of new durable goods (both consumer and producer durables) that usually gets hit hardest in a recession, I think it is important to do something like this. Plus, I'm just curious to see what difference it makes.

Anti Urban Economics

I'm just throwing this out there. Read at your own risk. I don't know what I'm talking about (even more than usual). I'm just thinking out loud, and being ornery. I will explain where I'm coming from after I've made my point.

There's a difference between "strategic complementarity" and "positive externalities". Strategic complementarity is what creates cities. But cities don't necessarily create positive externalities. "Network externalities" is a bit of a BS term that conflates two conceptually distinct things.

Here's a very simple abstract game to illustrate the difference. (I think I stole this from Cooper and John [Update to fix link:JSTOR link Here, Working Paper version link Here.])

All agents are identical. Each agent has a utility function U(x,y), where x is his own action and y is the action chosen by others. In symmetric Nash equilibrium {x*,y*}, where each agent chooses x to maximise his utility taking y as given, and all make the same choice, we know that U_x(x*,y*)=0 and x*=y*. (And U_xx(x*,y*) < 0 for the second order condition).

"Strategic complementarity" means U_xy(x*,y*) > 0. "Positive externality" means U_y(x*,y*) > 0. Those are different things.

Strategic complementarity means if others do something, that increases your marginal utility of doing the same thing. Positive externality means if others do something, that increases your utility. Period.

Here's an example with strategic complementarity and a negative externality:

Negative interest vacuum-cleaner Gesellian money for broke central banks

[I can't decide whether this thought-experiment has any policy relevance. I hope not, but who knows what the future will bring? It came to my mind after reading a (more policy-relevant) post by Simon Wren-Lewis.]

1. Helicopter money is when the central bank prints money and puts it in people's pockets. Vacuum-cleaner money is the exact opposite; it's when the central bank takes money out of people's pockets and burns it.

2. Paying 5% interest on holding money is when the central bank pays you $5 per year for every $100 you have in your pocket (or in your account at the central bank). A 5% tax on holding money is a negative 5% interest rate on money; the central bank charges you $5 per year for every $100 you have in your pocket (or in your account at the central bank).

3. Let's put 1 and 2 together. "Positive interest helicopter money" is when the central bank prints new money to pay you interest on the money in your pocket. "Negative interest vacuum-cleaner money" is when you pay the central bank interest on the money in your pocket and the central bank burns it.

The equivalence between national debt and transferable monopoly rights

I got this idea from reading a Matt Rognlie comment on a previous post. (But Matt may or may not agree with what I say here).

A. Suppose the government sells bonds, and finances those bonds by imposing a 10% sales tax on (say) milk.

B. Suppose the government sells transferable milk quotas, and sells just enough milk quotas that milk prices rise 10% above marginal costs.

C. Suppose the government sells transferable local monopoly rights to sell milk, and those local monopoly rights cause milk prices to rise 10% above marginal costs.

A, B, and C are basically [weasel word] all the same. For any tariff there's an equivalent quota, and quotas are just one way for a cartel to implement monopoly pricing. In all three cases the government is creating a marketable asset financed by a wedge between price and marginal cost. [Sure, it makes a difference if the demand for milk is uncertain, so one of those assets might be riskier than the others.]

That's basic micro. Now let's do some macro.

Fencing In Canada

Wisconsin Governor and potential presidential candidate Scott Walker apparently thinks it is not an unreasonable idea to consider building a wall between Canada and the United States in order to secure his country’s borders from security threats.  Now, to be fair, he did not say that a wall should be built along the 5,525 mile long border – only that it was an issue worth looking into.  According to Walker: “Some people have asked us about that in New Hampshire.”  This of course comes on the tail of Donald Trump and his call to build a wall on the US-Mexico border – and have Mexico pay for it.