HowTo: Consumer Behaviour. Or, the economics of my wife’s coffee-drinking

Eco 1 students: we’re about to study this sort of thing. Sort of.

So, the other day, my wife calls and asks me to work out her coffee costs. Two cafes at Columbia University, one in (after a fashion) her Art History library (call that one cafe A), and another … elsewhere (okay, I wasn’t really listening to that part – call it cafe B), but near.

Cafe A charges price PA = $3 per cup – but every tenth cup is free. Cafe B charges PB = $2.55 per cup. My wife wanted to know which was cheaper, and a third option, which was going to Cafe A and B in about an 80:20 ratio.

First, I assume that, since my wife is a student there, she’ll always benefit from the tenth cup. Her average price then is actually PA = (3 x 9)/10 = $2.70 per cup. It will always be more expensive than going to cafe B all the time. If I put it graphically, suppose her options are anything from 100% A, to 100% B, and anything split between the two.

Coffee pic

And thank God I always tell my students that they don’t need to draw their neo-classical markets to scale.

As she hangs up (this happened a lot – students were rolling by, pre-mid-term), my wife mentions that a nice man in cafe A makes her prefer their coffee, though.

Ah. This presents a problem – the quality of the coffee is not the same. My wife’s enjoyment, or Utility, from drinking coffee at/from cafe A (call it UA) is clearly higher than that of/at/from cafe B (call that UB). Now, what to do?

I’m going to assume, ceterus paribus, that this man’s niceness is the deciding factor (and kill him. But first, this). Now, my wife is indifferent between A and B.

Do the prices PA and PB need to be equal, for this indifference? No.

Does the quality, measured by UA or UB, need to be equal? Also no.

What is needed is that the ratio of prices equals the ratio of the utilities: i.e. that price-per-enjoyment-unit is the same. This tells us the value of coffee from cafe A in terms of the coffee from cafe B:

If we normalise UB = 1, then PB/UB = 2.55. Then, if PA/UA = 2.55, as required for my wife’s indifference, and PA = $2.70, UA = 2.70/2.55 = 1.059. My wife is deriving 5.9% greater pleasure from cafe A, for which she is prepared to pay 5.9% more – hence a price 5.9% greater!

Now, this is on average. Cafe A is down a bunch of stairs, up which (either with coffee in hand, or having enjoyed it) to walk is a dis-incentive, particularly with a bag full of art history books. So that’s a negative Average Willingness-to-Pay Effect on price at cafe A. On the other hand it is, more-or-less, ‘in’ the art history library, which may make it more pleasant (nicer building, known students, what-have-you), so that’s a positive Average Willingness-to-Pay Effect on price at cafe A.

I’m lumping all of that into my wife’s Utility function, and calling it quality. It won’t all be the friendly man behind the counter, but the quality of the experience of getting/having coffee from or at cafe A is greater than from or at cafe B.

Students! What else is there? I have taken a fashion of behavioural approach to my wife’s indifference between two different cups of coffee at two different prices – but she is a price-taker. What might exist at the level of market demand for coffee from cafe A and/or B? Might one supply curve be higher? Might one demand curve be less elastic? Remember, we only know the market price, not the market quantity.

This is the stuff we’ve learned so far: how markets clear, and at what prices. What we’re coming to is why, or under what conditions, consumers decide to participate or not in that market, at that price.

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