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Inflation and the Prisoner’s Dilemma

01 May

To combat inflation, the reserve bank raises interest rates. Have you ever wondered why? What do interest rates have to do with inflation, after all?

At first glance, you might think raising interest rates should increase inflation. After all, when interest rates go up, zillions of people find their banks charging more interest on their mortgages. So : why do reserve banks raise interest rates to fight inflation?

The answer is surprising.

What causes inflation? Inflation is when prices go up. We all know that. So what makes prices go up? What makes things more expensive?

Let’s simplify the question, and imagine an economy with one company. The company has two workers. The company produces an incredibly useful thing called a “thneed”.

Suppose each worker earns $100 a day and produces 100 thneeds in a day’s work. To make a thneeds also costs $1 worth of truffula tufts, so a thneed costs $2 to make. Let’s imagine this is also the purchase price.

Since thneeds are so useful, the spend all their money on them, buying 50 per day.

A Simple Economy - Two workers producing "Sneeds"

A Simple Economy - Two workers producing "thneeds"

What we’re going to do next is see how inflation might come into this simple economy. Let’s assume that every time the price of thneeds goes up, so does the price of truffula tufts – and by the same percentage.

Now imagine that one of the workers is not satisfied with his or her income. There’s full employment, so it’s easy to negotiate a payrise. Suppose that the boss agrees, and now pays the worker $120 a day, but the worker is still producing 100 thneeds a day.

This last point is important, so please get it – the worker is being paid more, but is not producing more.

Now, how much does it cost to produce a thneeds?

The factory makes 200 thneeds. This used to take $200 worth of raw materials. Wages cost $220 now, instead of $200. The total cost of making 200 thneeds is $420, so thneeds are $2.10 each. Inflation! In fact, since we have inflation, the price of truffula tufts will probably also have gone up. The raw materials cost more that $200, which in turn makes the thneeds still more expensive, and so on.

When this settles down, we find that since half of our workers workers got a 20% payrise, the price of everything has gone up 10%.

To make 200 thneeds now costs $220 in raw materials, and $220 in salaries. Thneeds now cost $2.20 in the shops.

Now, worker 1 is better off – they can now buy 54 thneeds a day. Worker 2 is now worse off, and is forced to live with only 45 – so worker 2 decides they they, too, want a payrise. This raises the price of making thneeds even further – prices will have risen by 20%, so that making 200 thneeds will cost $240 worth of truffula tufts and $240 to pay the staff.

Finally, the thneed costs $2.40. The workers can buy 50 thneeds a day with their salary, so for all their payrises, they’re no better off than before.

In fact, they’re worse off, if they were saving for retirement. Suppose they each had $100000 saved up to buy thneeds after they retire. Before, that could have bought them 50,000 thneeds – enough to keep them going for quite a while. Now, their retirement savings can only buy 41,667 thneeds, and they may begin to worry how to support themselves. Never mind, they can always plug their boss for another payrise…

This is a classic “prisoner’s dilemma”. The best outcome for both is if nobody asks for a payrise. If both ask for one, they both suffer. However, if only one asks for a payrise, the lucky earner of the higher salary is better off, while their hapless colleague suffers.

Imagine you are one of the workers : here’s the tableau for the “payrise game”, showing how many thneeds you can buy under various circumstances. The tableau assumes raw materials are subject to the same price rises as thneeds.

Your colleague
No Payrise Payrise
You No Payrise 50/day now
50000 when you retire
45/day now
45454 when you retire
Payrise 54/day now
45454 when you retire
50/day now
41667 when you retire

Your colleague faces the same choice.

Like any prisoner’s dilemma game, no matter what your colleague does, you are better off with a payrise. But if you both take a payrise, everyone suffers. It’s the same in the real economy – everyone wants a payrise – but if everyone gets one, everyone suffers.

With only two people, you can negotiate and cooperate. But how can you get a whole economy of millions of people to choose the less greedy way?

That’s where the reserve bank comes in with their interest rates. I’ll look at this in my next post.

 
 

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