Skip to 0 minutes and 1 secondLet’s consider what the optimal level of crime should be. To some of you, this question may sound strange. Of course we want very few crimes, or no crime at all. But if you have some background in economics, you know that it's probably better to have some crimes taking place. Economic theory predicts that having zero crime at all, it's probably not a good thing. Why is that? It is because, just like all the other good things in life, having low crime is not for free. There are many things we can do to lower crime. Hiring more police, building on more prisons and rocking on more criminals or adopting more advanced technology to improve the crime scene investigations.
Skip to 0 minutes and 47 secondsAll of these things should lower crime, but they all cost money. So if we want to have a really low crime rate, we can try that by spending a lot of money on these measures. But that means we will have very little resource left for other important things, such as national defense, public education, and healthcare. Are we willing to do this? Where is the right balance between how much to spend to fight crime and how much to spend to have other things that we like to have? Intuition from the basic economic theory can help us answer this question. Let’s say I enter a coffee shop to buy some coffee and bagels.
Skip to 1 minute and 29 secondsEating more bagels and drinking more coffee makes me happier. If my budget is unlimited, what I should be doing is obvious. Just drink a lot of coffee and buy a lot of bagels as much as I want. But that’s not realistic. My budget is clearly limited and I need to figure out what's an optimal way to allocate my limited resource over consumption of coffee and bagels. Economists analyze this question using a simple 2-dimensional figure which represent my budget constraint and preference over consumption of coffee and bagels. This inequality represent my budget constraint.
Skip to 2 minutes and 10 secondsThe price of coffee times how many cups of coffee I buy, plus price of bagel times how many bagels I buy, equals to my total spending over consumption of coffee and bagels. And this amount has to be equal to, or less than my total budget. This budget constraint can be easily represented on the 2-dimensional space. Let me use the x-axis to represent my consumption of coffee and y-axis for my consumption of bagels. If I spend all my money on coffee, I can buy M/Pc many cups of coffee. If I spend all my money on bagels instead, I can buy M/Pb many bagels.
Skip to 2 minutes and 57 secondsIf I use up all my money on buying both coffee and bagels, then my consumption will be somewhere on this line. In fact, all my possible consumption choice can be represented by the points on this line and the area below the line. Now, let me draw this, the so-called indifference curve. What this curve represents is the set of consumption bundles that I find equally attractive. For example, at this point I have a lot of coffee, but very few bagels. At this point I have a lot of bagels, but very few coffee. But I may actually find these two consumption bundles equally attractive. There can be many other consumption bundles that I find equally attractive as these two points.
Skip to 3 minutes and 49 secondsIn other words, I am indifferent between consuming any of these points. When I connect all those dots, I recover this indifference curve. Let’s take a look at this indifference curve now. Again, all the points on this curve are equally good for me. Now, which of these two bundles do I prefer? Since this point here is just as good as this point, which is clearly worse than this point on this curve, I should prefer this point. And it should be clear that I would prefer to be on the indifference curve to the upper east, because consuming more coffee and bagels will only make me better off.
Skip to 4 minutes and 35 secondsThe slope of this curve represents how much I am willing to trade between consuming coffee and bagels. For example, at this point where I have a lot of bagels and little coffee, I am probably willing to give up a lot of bagels to get one more cup of coffee. Graphically, from this point, giving up a lot of bagels but consuming one more cups of coffee makes me as happy as before, because that puts me back on the same indifference curve as before.
Skip to 5 minutes and 9 secondsOn the other hand, at this point where I have a lot of coffee and just few bagels, I am willing to give up very few bagels to get one more cup of coffee, because I already have enough coffee! At this point, you may wonder what does this have to do the crime, but just bear with me for one more minute and you'll get back to it. So this straight line represents my budget constraint and these curves represent my preference over consumption of coffee and bagel. From this figure, do you see what my optimal consumption of coffee and bagel should be? Within all the possible consumption bundles I can afford, I want to go as northeast as possible.
Skip to 5 minutes and 58 secondsSo this point, where this line is tangent to the curve, should be my optimal consumption choice. Let’s change the setting a little bit. Suppose that you are a high-ranking policy-maker with a limited government budget. With this money, you have to do a lot of different things. You have to spend the money to take policy measures to fight crime. At the same time, you also have to spend the money to achieve other policy goals. Such as better public education, national defense, healthcare, and so on. Let’s change the axis now, so that the x-axis now represents the level of public safety and the y-axis how much money is spend on other policy issues.
Skip to 6 minutes and 46 secondsAs before, if I spend all my money on public safety, we would end up here and achieve this much public safety. On the other hand, if I spend all my budget on everything except fighting crime, we would end up here and have no public safety at all. So as before, our optimal consumption point would be somewhere in the middle, where we spend some money to fight crime and some money to achieve other policy goals. So with this simple graphical analysis, it should be clear that having no crime at all is probably not a good idea for our society.
Skip to 7 minutes and 29 secondsIt means we will have to spend too much on fighting crime and this just would not be an efficient use of our limited resource.
Optimal crime level
Tell us what you think about the following questions using the graphical analysis shown at the end of the video.
How does the budget constraint change when government budget increases? How does the budget constraint change in light of advances in policing technology? Predict how the optimal level of crime will change in each of these cases.
© Songman Kang, Hanyang University