## Budgets and Opportunity CostJanuary 19, 2012

Posted by tomflesher in Finance, Micro, Teaching.
Tags: , , , ,

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.

## Opportunities and What They CostDecember 23, 2011

Posted by tomflesher in Finance, Micro, Teaching.
Tags: , , , , ,

One of the fundamental concepts in economics is that of opportunity cost. In order to understand opportunity cost, though, we need to take a step back and think about costs in a more general way.

The standard example goes like this: I like books, so I want to turn my passion into a job and open a bookstore. To do so, I need to rent a storefront and buy some inventory; for now, I’m going to run the bookstore myself. I’ll be open eight hours a day, so I’ll quit my current job at the box factory and do the bookstore job instead. Easy peasy, right? I even have $100,000 in the bank to get myself started. Let’s look at the costs. The first thing to consider is the actual money I’m laying down to run this business. Say rent is$1,000 per month. If I don’t want to bother with discounting – and for now, I don’t – then that means I’ve spent $1,000 x 12 =$12,000 on rent this year. Then, imagine that in order to meet demand and still have a decent inventory, I need to spend $43,000 on books. That brings me up to$55,000 worth of cash that I’m laying out – my explicit costs, otherwise known as accounting costs, are $55,000. But accounting costs don’t show that I had to give up my job at the box factory to do this, and I could have made$45,000. They also don’t account for the interest income I’m giving up by pulling my money out of the bank to live on it. Even if interest rates are only 1.25 APR (that’s annual percentage rate), I’m losing $1,250 in interest income. So, for simplicity (I don’t want to bother with compounding, either), let’s assume that in January I take out this year’s$45,000 in salary and keep it under my mattress. I buy my inventory and pay my rent. I’ve given up $1,250 in interest income and$45,000 in salary, so even though I haven’t laid out that cash, I have to count it as a cost. Accountants won’t write down what I gave up on a balance sheet, but my implicit costs, or opportunity costs, are $46,250. Total costs are simple – just add implicit and explicit costs. My total costs for starting the business are$55,000 + $46,250 =$101,250.

The key to understanding opportunity cost is that it’s a measure of what you gave up to make a choice, and so it shows how much something is worth to you. If I offer you a free Pepsi, your opportunity cost is zero, so you might as well take it. If I offer you a Pepsi for your Dr. Pepper, we can infer two things:

1. I value Dr. Pepper at least as much as Pepsi, and
2. I can figure out how much you value Dr. Pepper, relatively, based on your decision. If you accept, then you must value Pepsi at least as much as Dr. Pepper; if not, you must value Dr. Pepper more (and would thus be rational, since Dr. Pepper is superior to Pepsi).

Opportunity cost is very useful for determining preferences. We’ll talk about that a little more later on. In the meantime, just remember this distinction:

• Explicit costs are things you paid money for
• Opportunity costs are how much you’d value your best alternative
• Total costs are the sum of explicit and opportunity costs.