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Budgets and Opportunity Cost January 19, 2012

Posted by tomflesher in Finance, Micro, Teaching.
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In the previous entry, we talked a little about opportunity cost. In short, it’s what someone gives up in order to acquire something else. What does that have to do with budgeting?

Start with the plain-sense definition of a budget. Most people think of a budget – quite correctly – as a list of planned expenses by category. I might plan out my week’s spending as:

  • $30: gas
  • $200: planned monthly expenses (rent, insurance, utilities)
  • $50: groceries
  • $40: a meal out
  • $30: savings
  • $50: petty cash (Starbucks, forgot my lunch, that sort of thing)

That comes out to $400. What does that tell me? Well, for it to be a good budget, I’d better not make any less than $400 a week! Otherwise, I’m planning to spend more than I make, and that’s going to get me into trouble shortly. (If I spend myself into a deficit, I’ll need to plan to get out at some point.) It also tells me that I expect to make no MORE than $400 this week. After all, I have a spot for savings and a spot for petty cash, so I have places for overflow. Petty cash is what some people call slack,where anything “extra” would go.

Let’s simplify just a little. Let’s say I have that same $400 income, but I can only spend it on two things: coffee and sweaters. Sweaters cost $25 each, and coffee costs $2 per cup. I have a couple of choices – in fact, an infinite number of them – for how I can spend that money. For example, if I want to spend all my money on coffee, I can buy

\frac{400}{2} = 200

cups of coffee. If I want to spend all my money on sweaters, I can buy

\frac{400}{25} = 16

of them. Of course, there’s no reason to spend all my money on one of those two goods. I can buy any combination, subject to the budget constraint that I don’t create a deficit: that is, that

2*(cups\:of\:coffee) + 25*(sweaters) \le 400

Think back to when we talked about opportunity cost: if I have the same budget either way, then think about how many cups of coffee I have to give up to get a sweater. There are a couple of ways to do this, but the easiest is to compare the prices: for $25, I get one sweater or 12.5 cups of coffee, so the opportunity cost of one sweater is 12.5 cups of coffee. Similarly, for $2, I get one cup of coffee or 1/12.5 = .08 sweater, so my opportunity cost of buying a cup of coffee is 8% of a sweater. Note that this is the same as dividing the total quantities I can buy:

16\:sweaters = 200\:cups

1\:sweater = \frac{200}{16}\:cups

1\:cup = \frac{16}{200}\:sweaters

Basically, we can use a budget constraint to determine opportunity costs by imagining that we spend our entire budget on each of two goods and then comparing the quantities, or simply by comparing prices. Opportunity costs represent budgeting decisions on a much smaller – some might say marginal – scale.

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